Class 10th Mathematics CBSE Solution
Exercise 7.1- Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii)…
- Find the distance between the points (0, 0) and (36, 15). Can you now find the…
- Determine if the points (1, 5), (2, 3) and (- 2, - 11) are collinear…
- Check whether (5, - 2), (6, 4) and (7, - 2) are the vertices of an isosceles…
- In a classroom, 4 friends areseated at the points A, B, C and D as shown in Fig.…
- Name the type of quadrilateral formed, if any, by the following points, and give…
- Find the point on the x-axis which is equidistant from (2, 5) and (2, 9).…
- Find the values of y for which the distance between the points P(2, 3) and Q…
- If Q(0, 1) is equidistant from P(5, -3) and R(x, 6), find the values of x. Also…
- Find a relation between x and y such that the point (x, y) is equidistant from…
Exercise 7.2- Find the coordinates of the point which divides the join of (-1, 7) and (4, -3)…
- Find the coordinates of the points of trisection of the line segment joining…
- To conduct Sports Day activities, in your rectangular shaped school ground ABCD,…
- Find the ratio in which the line segment joining the points (- 3, 10) and (6, -…
- Find the ratio in which the line segment joining A(1, 5) and B(4, 5) is divided…
- If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken…
- Find the coordinates of a point A, where AB is the diameter of a circle whose…
- If A and B are (- 2, - 2) and (2, - 4), respectively, find the coordinates of P…
- Find the coordinates of the points which divide the line segment joining A(- 2,…
- Find the area of a rhombus if its vertices are (3, 0), (4, 5), (- 1, 4) and (-…
Exercise 7.3- Find the area of the triangle whose vertices are: (i) (2, 3), (-1, 0), (2, - 4)…
- In each of the following find the value of k, for which the points are collinear…
- Find the area of the triangle formed by joining the mid-points of the sides of…
- Find the area of the quadrilateral whose vertices, taken in order, are (- 4, -…
- You have studied in Class IX, (Chapter 9, Example 3), that a median of a…
Exercise 7.4- Determine the ratio in which the line 2x+y-4 = 0 divides the line segment…
- Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are…
- Find the centre of a circle passing through the points (6, - 6), (3, - 7) and…
- The two opposite vertices of a square are (-1, 2) and (3, 2). Find the…
- The Class X students of asecondary school inKrishinagarhave been allotteda…
- The vertices of a ABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to…
- Let A (4, 2), B(6, 5) and C (1, 4) be the vertices of ABC (i) The median from A…
- ABCD is a rectangle formed by the points A(-1, -1), B(- 1, 4), C(5, 4) and D(5,…
- Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii)…
- Find the distance between the points (0, 0) and (36, 15). Can you now find the…
- Determine if the points (1, 5), (2, 3) and (- 2, - 11) are collinear…
- Check whether (5, - 2), (6, 4) and (7, - 2) are the vertices of an isosceles…
- In a classroom, 4 friends areseated at the points A, B, C and D as shown in Fig.…
- Name the type of quadrilateral formed, if any, by the following points, and give…
- Find the point on the x-axis which is equidistant from (2, 5) and (2, 9).…
- Find the values of y for which the distance between the points P(2, 3) and Q…
- If Q(0, 1) is equidistant from P(5, -3) and R(x, 6), find the values of x. Also…
- Find a relation between x and y such that the point (x, y) is equidistant from…
- Find the coordinates of the point which divides the join of (-1, 7) and (4, -3)…
- Find the coordinates of the points of trisection of the line segment joining…
- To conduct Sports Day activities, in your rectangular shaped school ground ABCD,…
- Find the ratio in which the line segment joining the points (- 3, 10) and (6, -…
- Find the ratio in which the line segment joining A(1, 5) and B(4, 5) is divided…
- If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken…
- Find the coordinates of a point A, where AB is the diameter of a circle whose…
- If A and B are (- 2, - 2) and (2, - 4), respectively, find the coordinates of P…
- Find the coordinates of the points which divide the line segment joining A(- 2,…
- Find the area of a rhombus if its vertices are (3, 0), (4, 5), (- 1, 4) and (-…
- Find the area of the triangle whose vertices are: (i) (2, 3), (-1, 0), (2, - 4)…
- In each of the following find the value of k, for which the points are collinear…
- Find the area of the triangle formed by joining the mid-points of the sides of…
- Find the area of the quadrilateral whose vertices, taken in order, are (- 4, -…
- You have studied in Class IX, (Chapter 9, Example 3), that a median of a…
- Determine the ratio in which the line 2x+y-4 = 0 divides the line segment…
- Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are…
- Find the centre of a circle passing through the points (6, - 6), (3, - 7) and…
- The two opposite vertices of a square are (-1, 2) and (3, 2). Find the…
- The Class X students of asecondary school inKrishinagarhave been allotteda…
- The vertices of a ABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to…
- Let A (4, 2), B(6, 5) and C (1, 4) be the vertices of ABC (i) The median from A…
- ABCD is a rectangle formed by the points A(-1, -1), B(- 1, 4), C(5, 4) and D(5,…
Exercise 7.1
Question 1.Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (– 5, 7), (– 1, 3)
(iii) (a, b), (– a, – b)
Answer:(i) We know that distance between the two points is given by:
d = √[(x1 – x2)2 + (y1 – y2)2]
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)
Distance between A(2, 3) and B(4, 1) is:
f =√ [(4 - 2)2 + (1 – 3)2]
= √[4 + 4]= √8
= 2√2
(ii) Distance between A(-5, 7) and B(-1, 3) is:
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)
f = √[(-5 + 1)2 + (7 – 3)2]
= √[16 + 16] = √32
= 4√2
(iii) Distance between A(a, b) and B(-a, -b) is:
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f = √[(a - (- a))2 + ( b - (-b))2]
f = √[(a+ a)2 + (b+ b)2]
f = √[2a + 2b] = √(4a2 + 4b2)
f = 2√(a2 + b2)
Question 2.Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2
Answer:
To find: Distance between two points
Given: Points A(0, 0), B(36, 15)
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)
For two points A(x1, y1) and B(x2, y2),
Distance is given by
f = [(x2 - x1)2 + (y2 - y1)2]1/2
Distance between (0, 0) and (36, 15) is:
f = [(36 – 0)2 + (15 – 0)2]1/2
= [1296 + 225]1/2 = (1521)1/2
= 39
Hence Distance between points A and B is 39 units
Yes, we can find the distance between the given towns A and B. Let us take town A at origin point (0, 0)
Hence, town B will be at point (36, 15) with respect to town A
And, as calculated above, the distance between town A and B will be 39 km
Question 3.Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.
Answer:Let the points (1, 5), (2, 3), and (- 2,-11) be representing the vertices A, B, and C of the given triangle respectively.
Let A = (1, 5), B = (2, 3) and C = (- 2,-11)
Case 1)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Since AB + BC ≠ CA
Case 2)
Now,
![](data:image/png;base64,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)
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fcoqeQkDjy1MjR1MpilNTIIZdmje/tst9wfFbfh/4I71y9lYdtym/dZI4C567bKep9KXvNZfex7XjJk/W4Je/kGdXn6rBHqet/D3s7oXeGyAAwIhmbTjXfKqwizhnvJ5jWo8371n7hMJQMoam/+rJJo9pVO0Ud75q9hs4doY05NvWh78t6rjrsaerzNKbsEA1tEW7pgz7TRlG/VTVQNbBVGqgOe7q5ZLLIohGDrlI1UDVQNVBcA9VhF1dxfUHVQNVA1cA8GqgOex491laqBqoGqgaKa6A67OIqri+oGqgaqBqYRwPVYc+jx9pK1UDVQNVAcQ1Uh11cxfUFVQNVA1UD82igOux59FhbqRqoGqgaKK6B/wK1solZMh4qzwAAAABJRU5ErkJggg==)
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)
![](data:image/png;base64,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)
BA + AC ≠ BC
Case 3)
Now,
![](data:image/png;base64,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)
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)
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)
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As BC+CA≠BA
As three of the cases are not satisfied.
Hence the points are not collinear.
Question 4.Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle
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)
Distance between two points A(x1, y1) and B(x2, y2) is given by
D = √(x2 - x1)2 + (y2 - y1)2
Let us assume that points (5, - 2), (6, 4), and (7, - 2) are representing the vertices A, B, and C of the given triangle respectively as shown in the figure.
AB = [(5- 6)2 + (-2- 4)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAbCAMAAAAqGX2oAAAAAXNSR0IArs4c6QAAAHVQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjqQOmaQOma2OpDbZgAAZgBmZjqQZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6ttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bi049mwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA2klEQVQ4T9VR2xLBMBDdVVVKEUqwqDaS//9E2W0ifTD6ZsY+ZDJnTs5lA/DLIfw0KYHbHb/HsZvHd0I7G+mjtwDuOkecslUIlCdVt78A6MkBjJp4BtOhK/gM0y08WbMNYYQp84/i0CredIRt1WPPhs9TKGnq8hyoxF5gamRduxY1WyGWIZhT0uveiGQqeSuCRRuzdIW3opS3xd5ax45OZZfhnuUBd3zH9lpSEpxiLEi/yzCeX4XteEdGiXTsKG6E8z6CqQvEpbRopWMYWw1XlvB0o7Gf/PTon7AXCFANHKkSoIkAAAAASUVORK5CYII=)
BC = [(6- 7)2 + (4 + 2)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
CA = [(5- 7)2 + (-2+ 2)2]1/2
= ![](data:image/png;base64,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)
= 2
Therefore, AB = BC
As two sides are equal in length, therefore, ABC is an isosceles triangle
Question 5.In a classroom, 4 friends areseated at the points A, B, C and D as shown in Fig. 7.8 Champaand Chameli walk into the classand after observing for a fewminutes Champa asks Chameli,“Don’t you think ABCD is asquare?” Chameli disagrees.Using distance formula, findwhich of them is correct
![](data:image/jpeg;base64,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Answer:It can be seen that A (3, 4), B (6, 7), C (9, 4), and D (6, 1) are the positions of 4 friends
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)
distance between two points A(x1, y1) and B(x2, y2) is given by
D = √(x2 - x1)2 + (y2 - y1)2
Hence,
AB = [(3- 6)2 + (4 - 7)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
BC = [(6 - 9)2 + (7- 4)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
CD = [(9- 6)2 + (4- 1)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AD = [(3 - 6)2 + (4 - 1)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Diagonal AC = [(3 - 9)2 + (4 - 4)2]1/2
= ![](data:image/png;base64,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)
= 6
Diagonal BD = [(6- 6)2 + (7- 1)2]1/2
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAAbCAMAAAD8vKfNAAAAAXNSR0IArs4c6QAAAIFQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjqQZrbbZrb/kDoAkDo6kDpmkGY6kLaQkLbbkNv/tmYAtmY6ttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bHHLStAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABRklEQVQ4T+1S2XLCMAyUuMxRoIfblJrWocRJ4///wFqyA3JpZpjwih5y2CvtaiWAeyQHLA6Is3v+9eMmK9un6qZ8NwPw5RxxknT4vZr2lvQF4uJTEpoXADPaQaNHXMCp1VHeex0AXXg9rRo9/hInb+HHBA1gkYBOPeftZPmOOBwDU9SLTquhsu2GSvXyX2LsOoKbYkltZbX5QvKTfOJgf364zT033W4Ql3Roxu+PiCvh32U+V2kKJKXttvPioIJ+r/GhgoNKosxps6K3kZ+f30fuhaaXwuE6AcCIAf6nn5NqYrFnK+k/EoAVE8r8T/6xPB/mGJfXazpg6xjQyx9n3Hkc3nF6nlanYepazSoo5YAzfrI+aWQfymhUU6jO9DrYP9mdTMnnF5DhmgdFYXEuNknkXPnZbuQmX5kkYfbvsg6ocU8Z4sAvz3Abpbz1Ak0AAAAASUVORK5CYII=)
= 6
It can be seen that all sides of quadrilateral ABCD are of the same length and diagonals are of the same length
Therefore, ABCD is a square and hence, Champa was correct
Question 6.Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Answer:To Find: Type of quadrilateral formed
(i) Let the points ( - 1, - 2), (1, 0), ( - 1, 2), and ( - 3, 0) be representing the vertices A, B, C, and D of the given quadrilateral respectively
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)
The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).
D = √(x2 - x1)2 + (y2 - y1)2
AB = [(-1- 1)2 + (-2- 0)2]1/2
=
= ![](data:image/png;base64,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)
= 2√2
BC = √[(1 + 1)2 + (0- 2)2]
=
= ![](data:image/png;base64,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)
= 2√2
CD = √[(-1 + 3)2 + (2- 0)2]
=
= ![](data:image/png;base64,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)
= 2√2
AD = √[(-1+ 3)2 + (-2- 0)2]
=
= ![](data:image/png;base64,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)
= 2√2
Diagonal AC = √[(-1 + 1)2 + (-2 - 2)2]
= ![](data:image/png;base64,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)
= 4
Diagonal BD = √[(1 + 3)2 + (0- 0)2]
= ![](data:image/png;base64,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)
= 4
It is clear that all sides of this quadrilateral are of the same length and the diagonals are of the same length. Therefore, the given points are the vertices of a square
(ii)Let the points (- 3, 5), (3, 1), (0, 3), and ( - 1, - 4) be representing the vertices A, B, C, and D of the given quadrilateral respectively
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)
The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).
D = √(x2 - x1)2 + (y2 - y1)2
AB = √[(-3- 3)2 + (5- 1)2]
=
= ![](data:image/png;base64,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)
= 2√13
BC = √[(3- 0)2 + (1- 3)2]
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
CD = √[(0 + 1)2 + (3+ 4)2]
=
= ![](data:image/png;base64,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)
= 5√2
AD = √[(-3+ 1)2 + (5+ 4)2]
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
We can observe that all sides of this quadrilateral are of different lengths.
Therefore, it can be said that it is only a general quadrilateral, and not specific such as square, rectangle, etc
(iii)Let the points (4, 5), (7, 6), (4, 3), and (1, 2) be representing the vertices A, B, C, and D of the given quadrilateral respectively
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)
The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).
D = √(x2 - x1)2 + (y2 - y1)2
AB = √[(4- 7)2 + (5 - 6)2]
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
BC = √[(7- 4)2 + (6 - 3)2]
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAbCAMAAADrnjcEAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjpmOjqQOma2OpDbZgAAZgBmZjoAZjqQZrb/kDoAkDo6kDpmkGY6kLaQkLbbkNv/tmYAtmY6tpA6ttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bgObRUAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA80lEQVQ4T+2S2RKCMAxFU1DrhgqKgEpFFm3//wdtKdAg4DA8OuaBGXpz0+Q0AD8fjIwOw0Icwwlg+CGb4MoX0pTsCZndBt1dOXIBmBWAiOwY9e3J4zp65FMM3NnKBP2tQiBXj1ysMyioKiy8uZkQu3pkJi/QxQZdLfmVqm4uintkhyCuZOAuJD99ouDxnUIgfInw7KgDVaN5dUs/pZEfacms5K6joAM0WnKZxQxgVlXW5TH58qSShWfHaJ143WC/q5Fz4iruOhK6wZv1eZeRJep7NUpBV0EzYLfDlszIEu1Ny/Xlhzt49ca6gBnuoz3/xJrAG4YgE9pXA5h6AAAAAElFTkSuQmCC)
= ![](data:image/png;base64,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)
CD = √[(4- 1)2 + (3 - 2)2]
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
AD = √[(4- 1)2 + (5 - 2)2]
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAbCAMAAADrnjcEAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjpmOjqQOma2OpDbZgAAZgBmZjoAZjqQZrb/kDoAkDo6kDpmkGY6kLaQkLbbkNv/tmYAtmY6tpA6ttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bgObRUAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA80lEQVQ4T+2S2RKCMAxFU1DrhgqKgEpFFm3//wdtKdAg4DA8OuaBGXpz0+Q0AD8fjIwOw0Icwwlg+CGb4MoX0pTsCZndBt1dOXIBmBWAiOwY9e3J4zp65FMM3NnKBP2tQiBXj1ysMyioKiy8uZkQu3pkJi/QxQZdLfmVqm4uintkhyCuZOAuJD99ouDxnUIgfInw7KgDVaN5dUs/pZEfacms5K6joAM0WnKZxQxgVlXW5TH58qSShWfHaJ143WC/q5Fz4iruOhK6wZv1eZeRJep7NUpBV0EzYLfDlszIEu1Ny/Xlhzt49ca6gBnuoz3/xJrAG4YgE9pXA5h6AAAAAElFTkSuQmCC)
= ![](data:image/png;base64,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)
Diagonal AC =√[(4 - 4)2 + (5- 3)2]
= ![](data:image/png;base64,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)
= 2
Diagonal BD = √[(7 - 1)2 + (6 - 2)2]
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 2√13
We can observe that opposite sides of this quadrilateral are of the same length.
However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram
Question 7.Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Answer:We have to find a point on x-axis.
Hence, its y-coordinate will be 0
Let the point on x-axis be (x, 0)
By distance formula, Distance between two points A(x1, y1) and B(x2, y2) is
AB = √((x2 - x1)2 + (y2 - y1)2)
Distance between (x, 0) and (2, -5) = √[(x- 2)2 + (0+ 5)2]
= √[(x- 2)2 + (5)2]
Distance between (x, 0) and (-2, 9) = √[(x + 2)2 + (0 + 9)2]
= √[(x + 2)2 + (9)2]
By the given condition, these distances are equal in measure
√[(x - 2)2 + (5)2] = √[(x + 2)2 + (9)2]
Squaring both sides we get,
(x – 2)2 + 25 = (x + 2)2 + 81
⇒ x2 + 4 – 4x + 25 = x2 + 4 + 4x + 81
⇒ ( x2 - x2 ) - 4x - 4x = 81 - 25
⇒ - 8 x = 56
⇒ 8x = -56
⇒ x = - 7
Therefore, the point is (- 7, 0)
Question 8.Find the values of y for which the distance between the points P(2, – 3) and Q (10, y) is 10 units.
Answer:Given: Distance between (2, - 3) and (10, y) is 10
To find: y
By distance formula, Distance between two points A(x1, y1) and B(x2, y2) is
AB = √((x2 - x1)2 + (y2 - y1)2)
Therefore,
√[(2 - 10)2 + (-3- y)2] = 10
√[(-8)2 + (3+ y)2] = 10
Squaring both sides to remove the square root,
⇒ 64 + (y + 3)2 = 100
⇒ (y + 3)2 = 100 - 64
⇒ (y + 3)2 = 36
⇒ y + 3 = ±6
⇒ (y + 3) will give two values 6 and -6 as answer because both the values when squared will give 36 as answer.)
y + 3 = 6 or y + 3 = -6
Therefore, y = 3 or -9
Question 9.If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM5OAAAkpIAAgAAAAM5OAAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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yclfI8aiV1meoE9EREAREQBERAEREAREQBERAEREAREQBERAEREAREQBERAEREAREQBE80/P7ff9EQBFEmbO1uUOdyhvj2Z+hIjApUIGFvIhCFnI5ZNue5Hb3Z3c2VoxxLBTRsZZklZ9KXpofBsLHIzEikqMC7XuEAwcIS7JjHcmpbe1Ts7vyWc1cP9cS1o7/8A15GlsHb+LI2HTW+63HrNsisXXbvFvXPyIO0cGV+MJJhfkWdhzGMu71gANeVZZGCqLdQCxBFXfYw+pZKF9l7/IfIvIA9v3Yxp8ForE5O7MlK5pyW3VdZFjToOT9rkiOIyOrtZzuZRIXkPhzoQPESceazItvlkYJc8UDbF6fgEa0ty9I9B9ddZ7uSvwnZb5cnd3jONSYHw3UvzxVJfMPJLPzNyLNIM/XZX3CX2TVA8jP0nipC7hB4SF0V6YuIjIHOpR704/iY0doiLehQJ2nwdytWVw5ni/adpw6r3Mjm2NJZSxj5Phi2ROiSOzGGO1T7ZoNRqQ0HI0szyfuV1QYe3CDDwfF2BPUkWXa/N/Bc/FLa8bGW8JmDp53EuMoP3cTXfdc9WG4mcbBb6gMZ+4vbXwaGfjfp67OIvK8A9sa1ccMFevOuKW8XRJGMEgzJF0Mx0CxDGg5sOFwvG8YCI0BgY58ZdnR6d8bIJhzQPMDNYQvbk6EG17rDjtzkzvtbd/t58t3vNroCvO+O/UTlWy/586IgXlYXe778rqEcwRO5ztOQLmZrqZGqwI656ZzasMFlSd3bcT6R/Nnpk2fLQk+v8Vi9mQtHh6fMnpu9OGDDTFXc6RL597MdXC275wbuo5uLy2DZKvxZf4DQz4hB8ka+n842jGHA0XDXwblcdpiLBQblrLdsTLhzSdnsSRAaoi6JIxgkGZIuhmOgWIY0HNhwuF43jARGgMDHPjLs6PTvjZBMOaB5gZrCF7cnQg2vdYcducmd9rbv9vPlu95tdEQBERAEREAREQBERAEREAREQBERAEREAREQBERAFwUvExY/FicHOR5iLwcuYXUYLxAqZG4gFi8dfNDIyvY2VMb3g2GV/ZCNkcNhjfh8gwZNbe1cmXXv1q4rveLnSICvG3hzNDFbt/gqTMfH+K3Jd7qDbQy+V+F3LH4pSlMnJlTOM74Wu18joYFVtOKJR5XxybLJDWUuk6z17mgvm8bOwZThm6mx3LzvSCg7Z93s2dAwLI5R1bzEJ6N9L7MmvMh1kiGD5kg7EwtLUXHkmS9JXNo7xzF0bMjKRGXV+qXE1gaw2IIgOCiBYLH4sMHAMQsReDlzC1E4gXir23EAsXjr5oY3pkJBV8ZM+wyv7IRsjhrvjCQD+fJrb2rkxbFmzXFd7tc6UDSngOBcpISydA2u/cbTqXk7qVmU38k/KkcFsjEhM75996KJ0AHgPKYC6ces/wAWLsY29dVwrOGaMcxqbmESVCjp/uLcXH6yb3Dz9f8AEZ9jwH6wjPJS7dfJX4xACyNZOjfUyZLc7rR34xk2XpsIZQAxQeZ3wj2jqEekJJ6EMiZ7G4niLh0t2MGcuIwLEkUZoK6i566TqW68GTQByQRglzDrygCsz1hxSdCrm+WOtrYITdEjnXVkeFjzHnYSxl3o+lMUEi8aKxckFSUawFgsS6utJlAEREAREQBERAEREAREQBERAEREAREQBERAEREAWhZuOJRARdv2YohkinQ2ICTRFWgeajaPo5GRLK76TvkaTyXjM3e7HkfiEddWlr1TZ9jEPneXbNd8y7ITAUmZ8N47ZvpeGSvjHfWn3pZdWn4f6tfxU11cNNVXZN/JGpS0u7SK77WP1KpQvtvf5D5G5CHXCtg0+DEWCkmdmyjVpvtuq6yNGvQUn7XJMcRqdXajnczCItIfD/QYcJE481mRbklkZJtiKRrGD0/QI1pTJ0j0F111ju3+WrabpcnZ3jONCcHw3e3niqSeYuSWfmbkeaQV9uyPuEvxzVA8iPsmCpG7A54RF8WaYuIjXWNjaTuwJZnTrDQ58kX1ED/rwC9eeTI0BdjVOutCjiWLeKRByZ3uRQSY7TN5y8LsoKOhuQxoNR9dSnQlxK+R7gCRazFlFb8cm2gK6h6ghn14pg5ntO/8cQ69RgY5ljvLFUwWRJJ2rCHFcgQow3igfK7ueRxYC2kALkl54vpaWDeK/KRvWCzJkv2Mdt+0xVZ09yupJv0dVr+FYcpeiWk140+kW5fXT3VGYM1NHLuUUbcWvWhl7U4vvicLZerxLhP3eco7OUMc/QDzUMuQJztCcSwCFvRFuljoIQrGorFQk5kO60tDU5E7gwgbIOMl79tMTE0M2Z+yWXbOXA0MuPNsXWYMGvh3rWlvm76+a18/T6/01+33/vRVa+mlN8AysP8ARYDEDB1kCmvPc9PUYznFfZc6HfQUvgMiag615MVzTIJl0d06z3hBCx5Md4t+zyVc4lfsYX3awauDNmyZdiYcl9AgsTlQQCFDDNzo/SHtX4R/fjbmXpaZBDRsudsTdjqbSHDUWyABxpZddv46ZHWRysUw2YK5SDJWmjr58mLz11J8lWvxeW5mIppeIlZpeN5K4em//Kozu/H/AMN/+aY6fWta1ut8+Pr/AKnjz+fnxbd5/P8As91tbfN31+/in8qVtp58fX60/t+1V1uJjMJIhz1ouI2N6O+vIjhedNrqoKOtqdZncpU5x7SMcgKIfski+C4Ai86ksA583IyyPNH7GUSPF/MF5eMBpFbfnkkzeygiKd8ehxtbghFPcHNGvZSwH4/9SjrKBof1NfNWreyxbe8sctiIw2WeLvhjUNWyO5D+PHX27ae4pZbdSlKWU3S08SoSefU6qnL/AIfVtTp9M3O3E6tVZcJ8WZaUOMvPlKmdqo+Td/vDUerxs9/neqix5p48/h/xWV6CU5SfdSERENCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiICNM48uwb0f8rOEpBtN8pA7n+6NpVFCUviycYruMfg+AxvhvoSLCEQmeKaSC0M7SOmNsbSMLWmIpTKHmFhEKZ9odroPIP9+wFfjcGOQgXu2M2X3eXcCpLEhfnnsLfbb/AONvj00zfHFR7kaYZAwZLHUGiiF8/MfGYaR672D2yx1cK3iJSXyVYkiAhPGnc/OckHzFCzsXVhLpV7yb2HR5Rn7XsiXo7bcGpsdXEw3Q2OHzL/24AY3a0F9lZ+5ufZY56LsgUd7QFL5SMiZAQ45sLVEoxJGM7Az3F0zR0Cy9GhHsN9xRG8niI0eAZH8Gdmt6aMb2JmLQQsDzYPPba1kGr73DktwEzRq7dnsZ8Vvu4lV5x6jhG6t3KnTV5dH+vSjjTnruSyQ+gq3Y2W/4tQUjXsa45xdOxlfJb84PlTCRukru+axpjdxq+HYlGwiO7IoLALDEVeF/fwVF9aMvZ8fH3GRA3W3WPh9I7U7lXG+PQx1xtWI+0O4g5jyc+BoAXmuJ1F4nZemCfmXoMqzVB8RZzvG5TKMZDJHYegCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIjSah5TBG2C+XoP5r2Zn2oXC6hGToCbDboqWaWlJcQULZokj4JUyMLqFxAQ0YLyC9laqXD418vCuL2POuMYLsmWuSEMFenbtR3LfqJM51QXd+Y+w+gw7qSNm8EOZHjyaI+mN5EmRsmN0o/hFgo/gz1mNhJmPw6RY6k/CU27Ts919yOXY8dc9tPmn18/p/X48f8AH8fw8/X64srW3/608efwr9f7PpX/AGLy03dpWKrb0GW3FCqt1NdJX2fTx2VMYwU1Kl7pqr44yvFTl/qVNlnpKc4brbz4CRro/s+iaK+xtLumWB9x2DuWpM6UnlltfncQJJL6Fk+QCaRXnNYfuDWRGb+XXySSlQyyMQNTcFRKyltbZqWVpb4+vn71/X63fr/f6fms3XV8/l96f1f/AL/t/RYtvurT7fXx+Xn8fv8Ab8v7Pz+vV8LdNLn2WuHGE2qacbrPJUp98Ex/c7qnO+O8eGJ6/mQoZ+C+XWWc2bpVvjd8fJYEto0do7qYTBNJbGcVEMi0t+cHaI4NMT0lhqE38o9jLYTk8YRgLEOS16f7ve5PmUls2dZemryGdcdwpJTXMryDPM89DdOTx1fNzpG+Z3cg354mU7yuljUxvb+wjBA9tI2Ds4eM2Pj8MMGfLc21srrWWe7vrZUiuyuSnEdfDEp4naXTS30fDT2RN1c5dPPfo/nu/m5lhERUUsJLsEREAREQBERAEREAREQBERAEREAREQBERAEREAREQBERAEREAREQBERAEREAREQBV43cIM0UexscWzEdcUN2tWm9hhaN2QBN+NHV5aK2OQ+1uXLsjMD4yw+C5iCj4/SuwcSlnGxjL+U1OCY0lLYlTKKyYI2HIgK8KdSzTBN1zF1/zqe7+ljtppMnQfGUYyp0/Gch7dt9+FqteufIyHzDrqAz0jxMxYf7gNkjacuf4sGLR0OzdxybLRHqj2xLiLpbjGdgZklGGZFBZejQj2HC0XkiMC4aPAMj+DOzoyu+RkLA53IWB5sHnttdB/a91myW4CZo2tS/2M+K73e11CeSuL4xOTt8mOP3k/5g6IKbWu4k6I5vcxgQPTmrS1NIk0WzkImQ3I0CdN3DYPidAaLK9NxJOH7HB4hIs0K3RqY32E+MCbCKu3CYd1c+5KthXFN3fgFiuy6A0cwRuQ3BPUGvdWv8I0pjiacJEivmU5soytOR6k7oWFZziXEVSeYsgqCcJRqCsD+Xam/IO6ig7o/5ob4sM675SBVH6STFxUNF0WTjFlxj8Xzh1Ji57lQeD5nimkgtDM7EIdfJUcitpiKUxF4deQimfWIkBJZERAEREARFjzT86fzogMoiIAiIgCIiAIiIAiIkLt4/HuAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCjTOPLsG9H/KzhKQbTfKQO5/ujaVRQlL4snGK7jH4PgMb4b6EiwhEJnimkgtDO0jpjbG0jC1piKUyh5hYRCmfaHayWRAV32AXYfNF9ckSG+bsqE9CntWQnOxK3i3TQgx47q/weHuo8mraOTXkYA9kbBeMY362YR2T5Rkosejvor1ONXBZbgpNgUfnUjGBt8ehAjBHB/Y2V4cw4s2hTdKRPceW3A6OQmW5Qp/LgjIQDGWuRkI8gwTk4rfnxZLhQxINfLrbWfnCxX7V/or/AFKa6uGiqrtS3+QK0pc9VbhyDJOluJpPlQ6YSyCNiPtednlv5y6cKYxhO2Xm9id4235Zm4MiQkhqNWYlZ3ls2cL8VyOPMNuO7Jl2M2pTHmt19vt/YEbPnXbnx0NthsVyKPQM1dFl5cwtzBuRYEBpYTbIiDs72UXEWN6+dT+re8PouxMg0+4tkXY3ZxybutbbgsydZ/vPjzrySpu9dSQgMJn0rjN+dPThKt7m1vj7/A4y9QqL40i4GcZhioSM2ABwzw8vw01Mz0PYrObJuC8uQrzZQwzwElxFTDq71YKxy89YevxqynzpL0phEocR8Bv4nzYLABPvS4cwU58ynIdfFsdR20XVIgM1/aBR3HLh3CODWwHl9LSm6mOwcybOKKKk9PTcutNv0etc0k3VL01v3eHh+3hbRauN7He5apVddtOYo0Nc7fidJKjy1D6zi3OJO1Zmr4x1r5+1vn7/AJ1pT6/0+PP8vK0TOfQET85htZBmctuEBrKQj4e0W6jITFhWYG5e5WsokCR4BhDIRnUknxQ7XYtUYAwEaJCohy1vxag9lpbdWnVi9Mozm30q4r7Bmn1TYS6RO5/B4c4z1BSaB8cukjSkTm5zaQ6MYj5Jh4rd2OMwH9ukMSIV3Mssx7cVa5XKBo93mWHKZ10/mnNZ96yUUncpYfT0kpvBp9MohhjtEQkPoQc51bJU3J7Eo+KI0N41uPRLQ57dcfQFrpHLwZYrX+6Eb9gvH8DvmLtXFnxi2fKmstK29HatcVVL1OkqqrocJ8dNFdVKfE/5DhXZ6Jp5PJZfPTrb4Yr1dMtRtYTWGlDeI8Wo8JuuPqDQszHfJwi6CM/D7d2QXyLGcUGUjQmfwo2s8hx6NupfQGkQPnFrjOXg0gkVnZnusWXXxZlHS6jDs3YSXFbmHq7k/wClfr9/H0rWn6+P+fhdOU/aumNXmf0yx+dck7b5w7f9IDjkg5KpPj0SbvTDZyO2HcnGIdkmJ2Onisk0fsERWltClkkbP+0m0W2WUMMMdubV9nB3FqVr7Nn08eMdfp+FfH+3/er4Fy6quLbW1U4zhWNJqXUl/i3fdMd6ak9iaW+PlNfd4nj/AGdRpZny08+TW5+tFin2p/RT+pFR2MoiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAIiIAiIgCIiAx7Nv5U/ko6bnPEPV6K1OqKid2nO+GJ9iEM55qEBboZ3qLNUpwml429izWRYAIg128kre8MT2QC+2UCmbM9Yhfb1cRBvYqkWQu3SPhER5R02H7+n6L5LsbIJgIFkHTHbTIJETjWHigbPhXGWjDK/Y2IxFti90FDFixuuHNazkY/npTIMEGtZhfmDYr7/AAZ7b78ty2H4p+VP5Ii0EdzvnCG5Sl6EZwOA7IRSfzntmLpDrznIirC3A+/Jg7UWJXq0QxEWEEe3jaHcF7JqPxGMkb8wYM2zeK52C7Pky3yJRE/f5JfRJeSXYfv6v6tv4sIiID//2Q==)
We know, By distance formula distance between two coordinates A(x1, y1) and B(x2, y2) is
AB = √[(x2 - x1)2 + (y2 - y1)2 ]
Now, as
PQ = QR
√[(5 - 0)2 + (- 3 - 1)2] = √[(0 - x)2 + (1 - 6)2]
= √x2 + 25
Squaring both sides,
41 = x2 + 25
x2 = 16
x = ± 4
Hence, point R is (4, 6) or ( - 4, 6).
When point R is (4, 6)
PR = [(5 - 4)2 + (-3 - 6)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
QR = [(0 - 4)2 + (1 - 6)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
When point R is (- 4, 6),
PR = [(5 + 4)2 + (-3 - 6)2]1/2
= ![](data:image/png;base64,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)
= 9![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAAbCAMAAABP9I/XAAAAAXNSR0IArs4c6QAAAG9QTFRFAAAAAAAAAABmADpmADqQAGa2OgAAOgA6OjoAOjqQOpDbZgAAZgBmZjoAZjqQZrbbZrb/kDoAkDo6kDpmkGY6kNv/tmYAtmY6tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///byhP2lgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAq0lEQVQoU8WQ2RKCMAxFEwTcxbpEqmKL5P+/0ZQu4EwfnTEP7Z20ObkJwG9D4xQTmU/XXJvh8MqlTZX1REcAfuwRF3MYn1sAwgb6bSEqhl0LmhxIo9TF0JuojE+/O3feEpEcpL+gqxx2EWhr9/nZja/JHqtAs7UIHdqwivZZFW2anKo0q7Qe7TlzpdzGY1iVd6/sUvwwBbrGlUeTX21ID1/zzkbMb2/68D/1AZbKCQTKPJLUAAAAAElFTkSuQmCC)
QR = [(0+ 4)2 + (1 - 6)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Question 10.Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Answer:![](data:image/png;base64,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)
To Find: Relation between x and y
Given: (x, y) is equidistant from (3, 6) and (-3, 4)
From the figure it can be seen that Point (x, y) is equidistant from (3, 6) and (- 3, 4)
This means that the distance of (x, y) from (3, 6) will be equal to distance of (x, y) from (- 3, 4)
We know by distance formula that, distance between two points A(x1, y1), B(x2, y2) is given by
![](data:image/png;base64,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)
Therefore,
√[(x- 3)2 + (y - 6)2] = √[(x + 3)2 + (y- 4)2]
Squaring both sides, we get
(x – 3)2 + (y – 6)2 = (x + 3)2 + (y – 4)2
x2 + 9 – 6x + y2 + 36 – 12y = x2 + 9 + 6x + y2 + 16 – 8y
36 – 16 = 6x + 6x + 12y – 8y
20 = 12x + 4y
3x + y = 5
3x + y – 5 = 0 is the relation between x and y
Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (– 5, 7), (– 1, 3)
(iii) (a, b), (– a, – b)
Answer:
(i) We know that distance between the two points is given by:
d = √[(x1 – x2)2 + (y1 – y2)2]
Distance between A(2, 3) and B(4, 1) is:
f =√ [(4 - 2)2 + (1 – 3)2]
= √[4 + 4]= √8
= 2√2
(ii) Distance between A(-5, 7) and B(-1, 3) is:
f = √[(-5 + 1)2 + (7 – 3)2]
= √[16 + 16] = √32
= 4√2
(iii) Distance between A(a, b) and B(-a, -b) is:
f = √[(a - (- a))2 + ( b - (-b))2]
f = √[(a+ a)2 + (b+ b)2]
f = √[2a + 2b] = √(4a2 + 4b2)
f = 2√(a2 + b2)
Question 2.
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2
Answer:
To find: Distance between two points
Given: Points A(0, 0), B(36, 15)
For two points A(x1, y1) and B(x2, y2),
Distance is given by
f = [(x2 - x1)2 + (y2 - y1)2]1/2
Distance between (0, 0) and (36, 15) is:
f = [(36 – 0)2 + (15 – 0)2]1/2
= [1296 + 225]1/2 = (1521)1/2
= 39
Hence Distance between points A and B is 39 unitsYes, we can find the distance between the given towns A and B. Let us take town A at origin point (0, 0)
Hence, town B will be at point (36, 15) with respect to town A
And, as calculated above, the distance between town A and B will be 39 km
Question 3.
Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.
Answer:
Let the points (1, 5), (2, 3), and (- 2,-11) be representing the vertices A, B, and C of the given triangle respectively.
Let A = (1, 5), B = (2, 3) and C = (- 2,-11)
Case 1)
Since AB + BC ≠ CA
Case 2)
Now,
BA + AC ≠ BC
Case 3)
Now,
As BC+CA≠BA
As three of the cases are not satisfied.
Hence the points are not collinear.
Question 4.
Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle
Answer:
Distance between two points A(x1, y1) and B(x2, y2) is given by
D = √(x2 - x1)2 + (y2 - y1)2
Let us assume that points (5, - 2), (6, 4), and (7, - 2) are representing the vertices A, B, and C of the given triangle respectively as shown in the figure.
AB = [(5- 6)2 + (-2- 4)2]1/2
=
=
BC = [(6- 7)2 + (4 + 2)2]1/2
=
=
CA = [(5- 7)2 + (-2+ 2)2]1/2
=
= 2
Therefore, AB = BC
As two sides are equal in length, therefore, ABC is an isosceles triangle
Question 5.
In a classroom, 4 friends areseated at the points A, B, C and D as shown in Fig. 7.8 Champaand Chameli walk into the classand after observing for a fewminutes Champa asks Chameli,“Don’t you think ABCD is asquare?” Chameli disagrees.Using distance formula, findwhich of them is correct
Answer:
It can be seen that A (3, 4), B (6, 7), C (9, 4), and D (6, 1) are the positions of 4 friends
distance between two points A(x1, y1) and B(x2, y2) is given by
D = √(x2 - x1)2 + (y2 - y1)2
Hence,
AB = [(3- 6)2 + (4 - 7)2]1/2
=
=
BC = [(6 - 9)2 + (7- 4)2]1/2
=
=
CD = [(9- 6)2 + (4- 1)2]1/2
=
=
AD = [(3 - 6)2 + (4 - 1)2]1/2
=
=
Diagonal AC = [(3 - 9)2 + (4 - 4)2]1/2
=
= 6
Diagonal BD = [(6- 6)2 + (7- 1)2]1/2
=
= 6
It can be seen that all sides of quadrilateral ABCD are of the same length and diagonals are of the same length
Therefore, ABCD is a square and hence, Champa was correct
Question 6.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Answer:
To Find: Type of quadrilateral formed
(i) Let the points ( - 1, - 2), (1, 0), ( - 1, 2), and ( - 3, 0) be representing the vertices A, B, C, and D of the given quadrilateral respectively
The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).
AB = [(-1- 1)2 + (-2- 0)2]1/2
= =
= 2√2
BC = √[(1 + 1)2 + (0- 2)2]
= =
= 2√2
CD = √[(-1 + 3)2 + (2- 0)2]
= =
= 2√2
AD = √[(-1+ 3)2 + (-2- 0)2]
= =
= 2√2
Diagonal AC = √[(-1 + 1)2 + (-2 - 2)2]
=
= 4
Diagonal BD = √[(1 + 3)2 + (0- 0)2]
=
= 4
It is clear that all sides of this quadrilateral are of the same length and the diagonals are of the same length. Therefore, the given points are the vertices of a square
(ii)Let the points (- 3, 5), (3, 1), (0, 3), and ( - 1, - 4) be representing the vertices A, B, C, and D of the given quadrilateral respectively
The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).
AB = √[(-3- 3)2 + (5- 1)2]
= =
= 2√13
BC = √[(3- 0)2 + (1- 3)2]
=
=
CD = √[(0 + 1)2 + (3+ 4)2]
= =
= 5√2
AD = √[(-3+ 1)2 + (5+ 4)2]
=
=
We can observe that all sides of this quadrilateral are of different lengths.
Therefore, it can be said that it is only a general quadrilateral, and not specific such as square, rectangle, etc
(iii)Let the points (4, 5), (7, 6), (4, 3), and (1, 2) be representing the vertices A, B, C, and D of the given quadrilateral respectively
The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).
AB = √[(4- 7)2 + (5 - 6)2]
=
=
BC = √[(7- 4)2 + (6 - 3)2]
=
=
CD = √[(4- 1)2 + (3 - 2)2]
=
=
AD = √[(4- 1)2 + (5 - 2)2]
=
=
Diagonal AC =√[(4 - 4)2 + (5- 3)2]
=
= 2
Diagonal BD = √[(7 - 1)2 + (6 - 2)2]
=
=
= 2√13
We can observe that opposite sides of this quadrilateral are of the same length.
However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram
Question 7.
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Answer:
We have to find a point on x-axis.
Hence, its y-coordinate will be 0
Let the point on x-axis be (x, 0)
By distance formula, Distance between two points A(x1, y1) and B(x2, y2) is
AB = √((x2 - x1)2 + (y2 - y1)2)
Distance between (x, 0) and (2, -5) = √[(x- 2)2 + (0+ 5)2]
= √[(x- 2)2 + (5)2]
Distance between (x, 0) and (-2, 9) = √[(x + 2)2 + (0 + 9)2]
= √[(x + 2)2 + (9)2]
By the given condition, these distances are equal in measure
√[(x - 2)2 + (5)2] = √[(x + 2)2 + (9)2]
Squaring both sides we get,
(x – 2)2 + 25 = (x + 2)2 + 81
⇒ x2 + 4 – 4x + 25 = x2 + 4 + 4x + 81
⇒ ( x2 - x2 ) - 4x - 4x = 81 - 25
⇒ - 8 x = 56
⇒ 8x = -56
⇒ x = - 7
Therefore, the point is (- 7, 0)
Question 8.
Find the values of y for which the distance between the points P(2, – 3) and Q (10, y) is 10 units.
Answer:
Given: Distance between (2, - 3) and (10, y) is 10
To find: y
By distance formula, Distance between two points A(x1, y1) and B(x2, y2) is
AB = √((x2 - x1)2 + (y2 - y1)2)
Therefore,
√[(2 - 10)2 + (-3- y)2] = 10
√[(-8)2 + (3+ y)2] = 10
Squaring both sides to remove the square root,⇒ 64 + (y + 3)2 = 100
⇒ (y + 3)2 = 100 - 64
⇒ (y + 3)2 = 36
⇒ y + 3 = ±6
⇒ (y + 3) will give two values 6 and -6 as answer because both the values when squared will give 36 as answer.)
y + 3 = 6 or y + 3 = -6
Therefore, y = 3 or -9
Question 9.
If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR
Answer:
We know, By distance formula distance between two coordinates A(x1, y1) and B(x2, y2) is
AB = √[(x2 - x1)2 + (y2 - y1)2 ]
Now, as
PQ = QR
√[(5 - 0)2 + (- 3 - 1)2] = √[(0 - x)2 + (1 - 6)2]
= √x2 + 25
41 = x2 + 25
x2 = 16
x = ± 4
Hence, point R is (4, 6) or ( - 4, 6).
When point R is (4, 6)
PR = [(5 - 4)2 + (-3 - 6)2]1/2
=
=
QR = [(0 - 4)2 + (1 - 6)2]1/2
=
=
When point R is (- 4, 6),
PR = [(5 + 4)2 + (-3 - 6)2]1/2
=
= 9
QR = [(0+ 4)2 + (1 - 6)2]1/2
=
=
Question 10.
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Answer:
To Find: Relation between x and y
Given: (x, y) is equidistant from (3, 6) and (-3, 4)
From the figure it can be seen that Point (x, y) is equidistant from (3, 6) and (- 3, 4)
This means that the distance of (x, y) from (3, 6) will be equal to distance of (x, y) from (- 3, 4)
We know by distance formula that, distance between two points A(x1, y1), B(x2, y2) is given by
Therefore,
√[(x- 3)2 + (y - 6)2] = √[(x + 3)2 + (y- 4)2]
Squaring both sides, we get
(x – 3)2 + (y – 6)2 = (x + 3)2 + (y – 4)2
x2 + 9 – 6x + y2 + 36 – 12y = x2 + 9 + 6x + y2 + 16 – 8y
36 – 16 = 6x + 6x + 12y – 8y
20 = 12x + 4y
3x + y = 5
3x + y – 5 = 0 is the relation between x and y
Exercise 7.2
Question 1.Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2: 3
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM1MgAAkpIAAgAAAAM1MgAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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If (x1, y1) and (x2, y2) are points that are divided in ratio m:n then,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAY4AAABGCAYAAADbyHMRAAAS6UlEQVR4Xu2dCfB31RjHvxFhZMm0TYRQipowSrZUZKJNUomKFhTZZZ1kHYS0iKZsY7QSCe1ITEk0lhhNK4lpVbYky3x6n6Pzv3Pv773buetzZv7D2+/ec8/5nuec5znPuoK8OQKOgCPgCDgCFRBYocKz/qgj4Ag4Ao6AIyBnHE4EjoAj4Ag4ApUQcMZRCS5/2BFwBBwBR8AZh9OAI+AIOAKOQCUEnHFUgssfdgQcAUfAEXDG4TTgCDgCjoAjUAkBZxyV4PKHHQFHwBFwBJxxOA04Ao7AnBG4n6TDJL1N0l/nDESVuTvjqIKWP+sIOAJTQ+Bhks6TtJWkm6c2uVTzccaRClnvtysEXGLsCulpfscZR411dcZRAzR/ZVAI+MYf1HKMbjBOPzWWzBlHDdD8lUEh4Bu/veXgPNhZ0qMknSbpcut6Y0lbSrqvpJ9KOlfSfyWtKOmF9vz9JZ0i6cqc4Txc0osl/UPSlyT9M/PMmpLuI+l37U2ldE8p6SfG85uSfpvBcyVJl0R4xoMeMmaecqQ0efmDQ0Ug5cYf6pxTjesFkm6QdJukcyQ9W9J2kn4p6QJJHHRnGYM4VdJukr4m6VpJT7b/j63gqmiAMKGtJX1O0kcl/UvSO6Pf7y3p+5Kuk/TSVBNb0G9K+tle0vWGJ8z2OZLAOA/Po0aEmTOOHgg11SdTSYuM94GSdpf0IJM4vyfdTTtB2uSw4QD5d6rJ9bTxm0iMQ8ctCykH+IGSPiVpLbttnGn/jcMvtA9KeomkYyQdIeku+4Ebxy8kcQAeHj3/ZklHS7rDGM5DJD0v+p3bxm8kvVXScROinyp4biHpWZL+Y/MfOmbOOHog1FSfTCEtMlYkxh0lfVHSX2xzo65A7fBDSX+WdLIxDg6SrtsQJcYx4JZdp0dL2lTSiZKeazcOBIPvZB78it1EniTppug3GMKv7FZxpP13GBB9oZ56qEnan5H0oeg96Pbbkjay36dCP1XwZI8FxjEGzJxxdE2lib5XRbqpIi3isYT0c6ipGBj+XiZVvsKYxaslfVbSAZI4FLpuqRhHFUyzEuMYcMuuE7dJ2u2SuFWghoI5ICyEho3jJ/a3b6aDp0q6WNLmkn5gv8V97iLp85KeEun6eewjkl5kqq6/JSCeNSS9QdK9CvpmrXaVdJLdivIew54DM/xDhfGVwRO7zo/tb/8BYbbcabpxfLkQjeKBKtINeusy0iITR+L8vakgAhAHSXqTpCdIusXUVxwaqK/CVbtL0FIxjiqYxhLjWHArWiMOWGwOxDRwoMftMZIuk/RKSSdkfjtY0n6SNrRbaLZ/jMOoPLmBBDoJ37rRjOcp6GY1U7fB9PJaGcZxpwlFscqu7FgX4bm+pEtN9Xd6Tod9YbbcuTnjWC5Eo3igjHRTVVpk4nh2/DFju4DA0Wejp0YSS93GJjEOBbe667K63QjebnaMuB88o1BVPVHSFdEPSM4Xmq1ij5wPryrp15JgLvGtNHyrL/sGQ00leAQYFuFJtDpz3yAn+HDImLmqqu7uGuh7qaTFMN2VJf3cVA6oM7poY5YY+8St7togEJwtCRdc1jpuHPqbSdpEElJ4aKifLjIPLAzq3MBw1Q3M5emSfmTqKCTs0MK3+rJvdME4ivCE2WIjxOUZZsvexc5xvoEzZMyccdTdXQN9L4W0GE81T4/dNxRDlRiHjlvRumFz4GaBOjPO3RT08T+TlLVvfEzSTpFNZB9J34ik6B3s32ub6jN8m/dw94Xx/L0nQkpNP0V4gi82IeYPs13P/lBP0YaMmTOOnog11WdTSIvxWN8o6R1m34jz+qC3Jt9PF6qrLHapN35diXHouOXR4KIb6zqmbsI5AkNy3Pg3a49BfZXIXTc8gz2MQDduMSEIDnXXd03CxmGjr5aSfhbhiTcZsS3ggK3wdXaTDw4CQ8bMGUdf1Jrou21Ki7eaNwput3hNYQ8j+OsB5o4ZDJwcFHilZD2qcL/E+If/PgbVbLRwWxCk3PiMsarE+K2GuPFNjNAE0XXNiB9sLrGH2CEWr9E2ZhBHrZSN8EZwQKggBoTbAx5I8Q0C2nm3SdTH2vywnyGEEDuCt1W2TYF+FuHJ/M6QxK2LWBYCLImDCa0OZp3RjhvH2zq++u+nbWmRqzRqCfz4uU7zb/zv8UIhApbGN/GwYuPDaMJ/e40Z0In3eIa58H7SjK1tH4YpGUcdiXHdmriBK+oK3Jtx7yUSG6bddXuEuZ1mPeRQVXHYX10wINYBexQ3iiLvOmI98FYjLQnM5nijKwIAQwPzqdAPcyrCk99wWGHNwaNIVVcGs85pxxlH19sy3ffalhaRiIgGhylwW+BgwKOG2gX4niN1crihpohTTKDK4HAJvvzMGJ35VyXtKenLLUOQknHUkRjr4IbEiaqCADokevJF8b99MI6Wl+fuWye3ESTrkMcK5kAuLOaHeitmNFOin7pYVsGsF9pxxlF3aYf5XtvSIhscCRq9K/EcNGiG7+A1A4OIbxAEzXEg4GET8hLxDuotbh9IVU+LggnbQDEl46grMVbFLcYBlQ7BlVNhHF+XtK3VuwjCBLcN9PsEC14TTb4P+kFaRx35rh4N9Nl9UAWzXmjHGUcbR5f3ERAgCR7qrUdKepzFgITfMIQ+PjIGtoVaasbR1jjL9jM1xoHbNtHmCBQ0VJ7ksuKGFev0+a0P+im7Ll0+VwUzZxxdrox/KxkCRA6j4sFHPTSkOm4cJMTDpTeOAWg6kCFKjE3mNDXGAS3sbdI8keMkwiTvGTnO8lrX9NNkrVK9WxWzMI7OaMdvHKmW3vuNESBgjAAw0ml/3KFZiEBnm39E6+D0U26xOqOd5TEOfInRt+I210fK7HJwLX0K/ftrLVGbF5+vg2C77+CNg86WtSBClnoM3ooR6Gzzj2QRnH7KL1RntLOIcZBi+S2WuIzCLmNqSCiM/VVWRGVMY5/aWHHXfaZ5VKXIfjo1vDrb/CMBzumn/EJ1RjtFjANfa1wvcaMkyd0YG2MnuyeZPF3K7WcFiQgm/w7J3FIFAPYzs3Rf7Wzzp5tCaz07/VSDsjPayWMcBKWQZwb/fXzvx9pwiSRmAI8OIlq9dYsADIM/3HKDmpOoYspmtmkc73ZW6b/W2eZPP5VGX3D6qQ5fZ7STxzio+/t687Ee+wYnDwzVxSDCbJqE6svib5RFAM8Y6n6QhiQO7qKgzqejcqNl+5vTc51t/gGD6vRTb3E6o50s4+C2gRslm5tyj2NvzI/cQUTkUl/AW3oEUHMS3EWwVwgOZB1wxcR1Fv99b8UIvFfSyycUAFh1rZ1+qiJ2z/Od0U6WcZADntxEeFNVKZNYf6rp33yZFZBBTeJeVmnxxgPmHLut5n3pPZl602lHM57eiaynRC/q1edbehcEHuxCpNkmxcscmtNP9VXuhXayjIN8MqSEIIndojKgSI+7W9lQArsoG0pflBqliMsNlueoTRdeEqxh8Ca/DbehrLGVnC0QXlYlFcpdbmWxBNWXxt9wBBwBR8AR+D8CMeNA2kG9QNUv4iCKGoxhR4v+pJD9cRYVzIGOmouI0JONcRzREtZ8c2tTgYQcSASThUaOG+okXycJG03cKHMKcyNaFcbYpIERDKyo8H2ZvmHIjLOP+txlxufPOAKOgCOwEIGYcVC3Go+XT0gqOvDRUXOlPjRycSWb5VEWKEg2VdJCU7/hgJwaDXWXg28ebbUdTpFEqmEK7ITGbYPUzEW1i2Eqf7JMnHXHwHsY25kjjKpug2FwcwJrb46AI+AIjA6BmHGEXPvYBLgx5DVUUWRJjZOTHWQ1GbCLUMkKBkQ+ItRXbUjVa1nuftRTpKzmwMVbh9oQoVFNC++potrFHPYkwwt1JEa3UJkBYwTzNl8E3tfC1J2GWgBxhF20QTtLKgAiTXMoEzRHHEdeg7kQEBjbLk63oj3cANou0sMYYES02yXtYvElGLpDCUp+Iy0y46Y+RF50MvEoZGzdbCKuoL7pR7hjWxxyG5vfaajFBRlRV23QTmXGkcVnZbOJECxIKuDUDQ8TDPPk8w+3mVCl7UZTAeWNgRvH2hNiHKlx9v4dAUfAEShEoKqqKtsRKqmLzf0yrviWAvJVJf3aXGvj+tar2+2jyL7BWKamqkqBr/fpCDgCjkApBGLGEcpkUhu6bIoOSkKSORf7xs3RF7kRnNey6ooYE1Jzo466NPoWKrKzF9g3mOP5kq5vwTjOPPEcwzhft6FyI6oa7zVvjoAj4AiMDoE8d9zLzDMqOxlUQqSMwO0WrynePcvKgnIQBtXRKpJ2NQM2BmnsD5ebt1YTY/kOZntB5RTKmDJGXGy3k4TdI6/gO+64VKUjmrlpLQgwwFjfxKsK+xDBlU2wGB2h+YBbRaDNfdXqwLyzeSCQFwBICmxyO2WD9yj5yAFMZDkHNf/GswkX3eCtxMFKGmRsHrdaKu2QuoR+uTHUbUj7l0jaODKMY9CnJCk3CjJp5rXHWsoR5kTCQ2+OwNgR2DNKCdR0X40dCx9/DwhkGQdeR6h9NshI9QwNV1hsBTAForaReki9fpilRCBiGzXSSZKusrlQd/oM83TCLsFNpW5jrCTxWk/SsZKICMfLC1XZgTauvL5xL6YQPfaYvBtJ3fH4e/0jgNAC/ZG2fU7pZNrcV/2vYn8jmCv9NEa8KMnhMabayX6AG8W6xgiCuog+qLq3oqSrC+waRH5vIekLjUe8zL5AIrQrzbvqeLv9EACYbSHJ4UWSPtDCt72LYSGA8IItjXQysY1tWKNMN5o291W6UQ6357nTT+2VyUurTqwEEhxX4LaK72xrqqu6qqr1JWGIx54Bw6DBxE4zm8tuBTYD3kO1xk2KyHFv00Jg7hu/6b6aFjVUn83c6ac6YvZGHuMgUeCpFj1OIaSmDUMy0v77LWVInf6oWc0mQbIMbr94bmHw3lzSNTmdhkJOFzRUkdUZr7/TDQJz3vht7KtuVmm4X5kz/TRalUWlY0k7wu0D9VOTRt1vDnZsJ3UbwYUYtrlh0DDMH261HeL0J3H/O0niz0vHVkcdutjZMh2DOV5xNBwTtpRE3RYSR55rqknUlCEzMl5s5BMLN8PqXy//RlcbP8aDINSQtSDgsZI5bgQ8ys+g/pNt7Kv6X1/8ptPPUnyGSD+N1r6IcdAp7q0UP4JAyXhbpxHlzUHDZmvSiDHZ24zb9InHF9lui8bF2Mmhxdhva/Lhmb5L7i9S44Md9TVwt8aTjpQ03OA4KHHFhkFwO0VViOPEteYgwf/ndhicJFLB2BXj2N7igMAD5oAXIRjl4UHCz9StrX2VapxOP0uRHRr9NF73RYyDzjGEc2DjzdRmbY3GA1/QAYb6/SV9eGaeNm1higoELzWCQIlZ4bZxpv03gihD4xaICzSOFGRTvst+4MbBLZADlFthytYF46iCBw4guH3POUanCl5OP0v302joZ3mMI+Wm976HiQAea5tKOtG81rhxoIbCySBuuGJzE0FteFP0A15vlOqlbsqRiafYBeOoggdeTnNnHFXwcvq5Z4Own0ZDP844Ep9sI+w+zkbMrQI1FMyBol2hYePA5sTfvpk5tpm/bA3LVlBUOAs/fLIUEDt0RwHWZGyGgdUthVwGDxxKKO/KH7fdObcyeDn9LN1Po6MfZxxz3uKL5x6yDhMfQcr6uIVyvDgenJD57WBJ+0nasIFtLHS5mqnIOGjyWhnGcaelv4nVbHVWfREeuH2TPw3VC2UGvC1zl6eAmtPPMmqYFP044/AtXoRAyDqMgwR2jLhRwZCrNSlfroh+QHK60Kox7tEBtF2oqsI0FuFB3BPZmcm4MMdAxLyldvpZisqk6McZRwen20g/EbIO43KazeRL+hiCKjeRhEQfGt5sROnjgYVBHZ0trroxc2kTji4ZRxEeMEsyJuNEALNEssTOQf60OTenn6WrPyn6ccYx5629eO5kNeZmgX0jzgMV9LEkvMzaN4jsJ3Ym2ET2sYzGqaTwLhlHER7MlZo0gVmSS42/pi7oY6dMp5+lKzgp+nHGMfbtmWb8i/Sx61hBrb3MKB2PACM1xmgM6qTXD+6WaUa5LNFmF7mqFuFBzAIZDFDb3WJBqSQCzSthnAqHofXr9LN0RSZHP844hrblhjGeUNTrkJysw9uYQXwjSWREjhtpYMgpRgwIaiu8mVJmJO6KcSzCg6zRZIDmtrWmBUgWZTMYxuqmH4XTz1KMJ0c/zjjSb6KxfoFAyryCU6iqSGdflIqGwxxvKNJypA6E64pxsIZFePAbXl+op0izkpJRjomWnH6Wrtak6McZx5i2oo81i0CXjMPRnx4CTj8119QZR03g/LVBIEAcB0ZHCnW5pD+IJRnVIJx+ai6XM46awPlrjoAj4AjMFQFnHHNdeZ+3I+AIOAI1EXDGURM4f80RcAQcgbki4Ixjrivv83YEHAFHoCYCzjhqAuevOQKOgCMwVwScccx15X3ejoAj4AjUROB/9WCYkgXAnHIAAAAASUVORK5CYII=)
Let D(x, y) be the required point.
Now,
Using the section formula, we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
x = 1
y = ![](data:image/png;base64,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)
![](data:image/png;base64,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)
y = 3
Therefore, the point is (1, 3)
Question 2.Find the coordinates of the points of trisection of the line segment joining (4,–1) and (–2, –3).
Answer:
![](data:image/png;base64,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)
The points of trisection means that the points which divide the line in three equal parts. From the figure C, and D are these two points.
Let C (x1, y1) and D (x2, y2) are the points of trisection of the line segment joining the given points i.e., BC = CD = DA
Let BC = CD = DA = k
Point C divides the BC and CA as:
BC = k
CA = CD + DA
= k + k
= 2k
Hence ratio between BC and CA is:
![](data:image/png;base64,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)
Therefore, point C divides BA internally in the ratio 1:2
then by section formula we have that if a point P(x, y) divide two points P (x1, y1) and Q (x2, y2) in the ratio m:n then,
the point (x, y) is given by
![](data:image/png;base64,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)
Therefore C(x, y) divides B(–2, –3) and A(4,–1) in the ratio 1:2, then
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Point D divides the BD and DA as:
DA = k
BD = BC + CD
= k + k
= 2k
Hence ratio between BD and DA is:
![](data:image/png;base64,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)
The point D divides the line BA in the ratio 2:1
So now applying section formula again we get,
![](data:image/png;base64,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)
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Question 3.To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs
th thedistance AD on the 2nd line and posts a green flag. Preet runs
the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
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)
Answer:It can be observed that Niharika posted the green flag at
of the distance AD i.e., 1/4 x 100 = 25 m from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25)
Similarly, Preet posted red flag at
of the distance AD i.e., 1/5 x 100 = 20 m from the starting point of 8th line. Therefore, the coordinates of this point R are (8, 20)
Now we have the positions of posts by Preet and Niharika
According to distance formula, distance between points A(x1, y1) and B(x2, y2) is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXwAAAAyCAYAAABfwmBiAAANdElEQVR4Xu2dBaw1RxXHf8UhOBR3LxbcNUgJEtyhuLtrKO7uxT3BKRogOAQv7hqcUtyd/OgsXV7v7uzduzN3773nJC8v3/d2R/5z5uyxObMPQYFAIBAIBAI7gcA+OzHLmGQgEAgEAoEAIfDLM8GLgH2BQ8p3FT0EAoHAFiLwiKnmFAJ/KiS72/k0cDfgE+W7ih4CgUAgEOhGIAR+We44AfAD4GTAX8t2Fa0HAoFAINCPQAj8shxyaeCpwIXLdhOtF0TgRMB+wF+Ar8SHuyDSu9d0dd4KgV+Wye4FnCm5dMr2FK1PjcBRgDsCxwY+C1wSuEX6gB8E/HvqDqO9nUFgbbwVAr8sj70JOBh4edluovUCCCjcvwd8uNX2dYE3AAcAryzQZzS5GwisjbdC4JdlsG8BVwO+WbabaH1iBI6aPtQG2p8A/D21f5yk7f8JuFjr/yfuPprbYgTWylsh8Mtx1hmAzwH66YI2C4FjpjTa0wNnBX7aGv77gXMA5wZ+tVnTitHOAIG18lYI/HIccA3grsD+5bqIlgsicB7ALKuPtvo4VtLw/5EC8X8r2H80vb0IrI23QuCXY6onAn8GDhzQxbmAWwIPBP454Pl4ZDUETgvcBXg08IclmroI8DHgQcCTl3hvDo8Gj9VZhVnzVp/APwaglmqWQh8dCni46Nd18NyYXjT9nwa8LTPiiwL3AW4H/HZjZrf5A1V4i/vtB+J+dODN6QNx8w3z3weP1eXX2fJWTuBfBThp0oRODDwU+FkLO9OLzgvcCHg78ICBm6cu/PV700+n3/dswGE93Z8ReDVg9kfbT1x/xLvZo7hfG7jVAAFuiu2lUobOHzcIruCx9SzWLHlriEvneMAXgN8BfrkW+S1PCbwjaT9mpfx+PRjPptfzAaZkmoPfRVpQbwFeklL9ZjP4HRqICovplVqoT++Z9/UBD9Hdb4KDV8YBtPxsaxl30phlCR4bg9o076yDt7IjHyLwLwh8BngxcNueFi+UAlwW+nlctuftfsA8W62jG/dM07/dHbhsx0d0uxGaz+zMtlFZUaBbBmMv+f/+mJ7ZxFfcE18auW4nAd4HXAH4ZWEYgscKA5xpvjZvZWc7ROBb+OuZyW3z2ozG+ilAX6fC34DlrpIHrfxIPqsDADUvsz+eE4ey1s4i7gHdkV9OLsn2gMymuAzwPOBfrT/cI62d2TrLUi2BHzy27MpM/3xt3srOYIjAN+h4JcAo/3cyLRqovHzyXXvoaFfp8ykLxIyORXQJ4J0J0x/vKkgzmvdNgYcBau6Nm0Xft1atJ22bMgrul+MCumVMuR1DtQR+8NiY1Zn+nZq8lR19TuAP8d+3O2kEvr5+/aK7SG5oj+RbIdOCW4vIlE1Pal5uj+a491mFy02A46f87w/Af+8wME7iwS4zpN64Q6mcpfA4cyqMppvFj7RW6nuTu23R+pm88JiRzF1L4A/hsdOkhAGtca3SvRVdjc2JxSJX18jpz/a1UljU5K0suDmBP9R/b0dmpujG0G9l5o4+zrFkwMMF8PdY0gT/UUagjm277z0tnCclt9ai55yTWqOBcHPBu0iBfi3gZSkI7kUqFvFyc+oO+g3wuiTwdbltO5XEoymQJtYKypJUQ+AP4THxvHKyYpryEZ4vaMgSAB9Me6gvFlUSq1ptl8SiJm9l8coJ/KH+ezs6NfD1FMjy6Pkvsr13P+BHQ81VphtLCnxTo1b58Izp+yHAKXoqZKqtO6anpNjIoj50Gdw7fTiaOi4Ggp+dDmiJzR2A5wN3Tj7mMWPdlHdq4KFwM+XYFOOSVEPgD+Ex+eu5yQp9PXDC5Lpt5q52/zXgvoDKxjZTaSxq8VZ2jXIC/61JCxjiv/eQls/rdrjiGjTr7GQrPSAGBrfNr19EWi66fPTtqaEvIl02PwS+2Prj/QFzwV0La7i4qa2zL97tgGKlaVbtpgYefkQVxrrZSlINgZ/jMZUz96huHGs9qYAYmG67qa6aspdWtdZLYjlF2zWwqMVbWTz6BP6y/vtXAJ5A9BCLpvEukngqqA1yqx0tIq0XN5gHfszD7/ooeBCrXWbB4LnmoW3XrsWuyWtt+JyC0LXmuvrUIseSAqw0HpY9tljaxYEx2TfN3LTuzOLpckdqrdwwKQVdMR7X1wyvsQH9HI+pLEierblBOgui+/YbrQV6fOLRCwClD5qtk79qYDEVb43dP/97r28Du9D6jHP59zZ2qpTWpklsMFJG2kU6S/Kvu+m7KLcZF73XfHw9pGX9l9p0uuQ6Givw5aMua2bMXErgoRbmPFcV+AbrdYWaFrmIhgh8Dzeqcf9kDDgpjpZTKpqmtUgNhretcj9WuiF0y+oWLU1z4a9SWEzFWyuvQ98GNu1MLUOfZl/+vYMw0OUhIrXWd608qs1twBOZ1sQxGNZFOXN70Xu6bjzj4CGt9oUcm4vUaiMvgUcts3sOLp0G/X2Br6aUVD8wDZ08afu74L+vgUUt3sruqj6BP9R/7ylEhbyRfrXPKdwN+qnNRDGQNJa0Mjw0YzZMLfIDqVb0yJ4OLbmr9uVdt33H+dtN3DNV0hSX9ulMtTJPbU6BeS2MpuhnajzcBx9KGvU2BG2H8pi5+qahas17d0NDug3fM0G23RRrXauNUljU5K0sVl0Cf6j/XvNX3+wLkrCfKnioSWkwZZUsHf3f+kCnGlMWzLR5DHx5qKqLmpQ5L8Q202Yv+Xd9wKZfmoXjGr0b8LYlP2DNfCxmpy+4rZnZVvWLkYcAs8Izq+Jh1+ZCf7fnw2hs5JDkvixd9riGhp/jsWY5rpniSLpUjD01pMVuEoZ+fW/32gUqhUVN3squU5fAb752Xf57ffZqWdaLsYZ7n4DLDmIDHrAYmj99wWgX9ufphiR/95EbysqLWkd769+fPwkfMXXT+W8/Ivp+mwwSN7QZO/r0m7LUa7sYufD6jcVDvM6ePqqejVCL7Sr3YezF0gquR+kDgzUEvkvSx2PNkmkxGlCXt5uArTEmD1Bq8eii3BUqhUVN3squVVvge6JOl4wTN/AqY34f+EhLKBnRVrD51TfybH3wvafzsp1u2ANiYQxDLPShd5Gni01z22/A/LSMNJnPuUez8lU1dH1+CnOxdR1M8bTC4ifTqUeFl2NSa21obRcjD5jvKo+MwcMccmNQCnHTCq+XfncJfFNkH5zSXEtrtLUEfh+PNevh/vfciB/GFyZLyBiTSpyBZ3lwL22bBbkKFr6bsx5r8lZ2n43Nusg2vCUPqFG/Kl2SodBV+LdT19rTVMCoIepmyVFT2Oqg5EbY+7zaurX0TYdrTG3Xytt0jpby+Nt++7VejJyb7AR/XxaPdpcKNG8TU/AvEvhNgSsvLH/UBGPNNVFL4Od4rD1OY2XWDrJWlnGh1yTLsp1avK0W5N71GoLFUOuxNm/leG90XnW24S14QE3dQ023Ti4rfeW6ah7eMTc3ic+rKQ0h85+tia5rZ1Uraa0XIw+Z7BqfyQl811n3mRpx+3KfUkOuJfAdfx+POW/dsrp+mqKICvWD04fR4HU7/rWtFqQ4LYPFMtZjbd7K8mxo+P0Q6XIxbU1SILw0MceirJhvAm6Kj2dRP/wBXWhekmJ+updwrEpruxh51YEXfr9P4DeXVOi2NEBeg9QOPdSkC6m0+6iPx3THXj3V5W9SfdXujdvputSF2dC2W5DLYNHmkbnxVpZ/Q+BnIfq/B76dNP69ufAetFLgm7+8zD0AmtEKfDUxyy1MTZt86fZUWPRtyusA/gy54nCq8dRup4vHjNcZoFajlwyOPyPFPtolPfzbtluQy2AxVODPkrdC4C+3/awmaNT9Nntes9aLgsXspmXJ1DfvAvYybStgTkWbfOn2VBjYTpfAF3frEw29xHzKMdVuaxGPmauvu1Irw5O2ZouZhdbFg9tsQS6LRbN+G8dbIfCX23r678z8sOZK+z5Sg30yjaeNx5ABWjefDLQ3TXNMe76zqZduj51v13uLNqXB7zsBj61wr+zU8xnbXgke23ULcuN4KwT+8tvHQ1CWi20XA/OyDDNuTFWdA0156fYc5rPKGHJB21Xa3uV3w4Lsth5nyxch8JdfmgPSLVQeOpMMaB2WgrreB7BumvrS7XXPZ9X+Q+CviuDi98OCDIFfhrNm1qqajel75nVbusGTiV6CbYnXdVOJS7fXPadV+w+BvyqCR34/LMjDMdk43goNf9xmMCffrBpzmD3U4wYwcLtOKnXp9jrnNEXfBwI3y5y0naKfXWkjLMgjVjoE/o5wvTn5Cn1rkOjPN13T3Op1UclLt9c1p1X6tdCc19aZZ79/Kk+hFeYBN6vAWqIiaHkEwoL8f8xC4C/PQxv7hqcT1eytN6JwseBUUCCwrQiEBXnkld046zFcOuO3pwWmvEDCPG4LKB06vql4MxCYNQJhQR6xPBttPYbAH7/PPFX7+RTA9ZRiUCAQCAQCs0YgBP5qy2PRLW+g8vL2oEAgEAgEZo1ACPxZL08MLhAIBAKB6RAIgT8dltFSIBAIBAKzRiAE/qyXJwYXCAQCgcB0CITAnw7LaCkQCAQCgVkjEAJ/1ssTgwsEAoFAYDoEQuBPh2W0FAgEAoHArBH4D+bOnmC+yK3LAAAAAElFTkSuQmCC)
Distance between these flags by using distance formula, D
= [(8 – 2)2 + (25 – 20)2]1/2
= (36 + 25)1/2
=
m
The point at which Rashmi should post her blue flag is the mid-point of the line joining these points. Let this point be A (x,y)
Now by midpoint formula,
![](data:image/png;base64,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)
x =
= 5
y =
= 22.5
Hence, A (x, y) = (5, 22.5)
Therefore, Rashmi should post her blue flag at 22.5m on 5th line
Question 4.Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).
Answer:Let the ratio in which the line segment joining (- 3, 10) and (6, - 8) is divided by point (- 1, 6) be k : 1
Using section formula
i.e. the coordinates of the points P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2,y2), internally in the ratio m : n are
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore,
-1 = ![](data:image/png;base64,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)
⇒ -k – 1 = 6k – 3
⇒ - k -6k = -3 + 1
⇒ - 7k = -2
⇒ 7k = 2
⇒ k = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAAAAAAAAA6AGa2OgA6Oma2OpDbZgAAZgA6ZjoAZrb/kDoAkDo6kDqQkLbbkNv/25A627Zm29u22////7Zm/9uQ//+2///bhcdSeQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAV0lEQVQoU4VOSRKAIAwL4ooLokj//1NbOnJxBnJJ03QJ8OFajBmANB8Inc/dp1c+x0yBbVFKkSk6pMkwXDnTKmSa0Rr7+bTKmgXtN2jTXBKBUaStyfrHF3tQArKHJie7AAAAAElFTkSuQmCC)
Therefore, the required ratio is 2: 7.
Question 5.Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.
Answer:The diagram for the question is
![](data:image/png;base64,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)
Let the ratio in which the line segment joining A (1, - 5) and B ( - 4, 5) is divided by x-axis be k: 1
Therefore, the coordinates of the point of division is (
,
)
We know that y-coordinate of any point on x-axis is 0
Therefore,
= 0
k = 1
Therefore, x-axis divides it in the ratio 1:1.
Division point = (
,
)
= (
)
= (
, 0)
Question 6.If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Answer:Let (1, 2), (4, y), (x, 6), and (3, 5) are the coordinates of A, B, C, D vertices of a parallelogram ABCD.
Intersection point O of diagonal AC and BD also divides these diagonals.
Therefore, O is the mid-point of AC and BD.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAACJCAAAAAB255f4AAAABGdBTUEAALGOfPtRkwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAB2MSURBVHja1XxpkFTVtqYd/b9/dHRHR0fH64jXN+69XnEeEQTBkVEGERAFURARFRFREBREGQQnJrkoKMoMiswgs8wzFFjIDAU1ZWZl5pn3vPfqtU9NXouiqjTjFe9ERQ1ZJ8/5ztprfetba++dN0CjHkZypRVopkQZV26kr3XyDY2LVUbGBEQLIwVxsjoy1zFWTQTPSJbRNASVAkWvY6xoWBEBywCcXrwvSMnoesaqmJaMqcTcJat//uwTCK9jrEZpEBnOF/T5RZbN+ZCy6zm2mI5kYPKfmwe+754k/DrCariqxsmlMSRrTbnyjoNSGVcAN8poYJGWICQAp6B0FAjWKFgF0qlSUgom8buWXmTSZTD/r5dBKBmkgSnJgLiaUhkGRhKtJCV4RqP4gOEC0UolpKEe0wHTbtJsvGdbxF3gjkJ7oi0ZMAJeSjFGAylpFKpGsatWlu+NYQwE4UKFOL7hkVf74fAXbkOoSmgdEkk1cQUto1r5WcbL89l/MFZNEakQkjLBoyAGnfftgpOZXwZ/tnTd+h1ahkoBz+DQC0eQhISzp7nUAZGNYVcJhhGlpYhxXlz6Rs/e/+2hJMhzi7fsPS/YqUv2gdDc0qHGJaU/rTpOShwlTGNgVWAo4hVgShcMePLJnqMG3XDjUDR3TAxwfFYZMBNzhG8IdT/98LJg25dT32s4VlPrH/V2gvidxevG9WnfY+CoeYeWvfBku/lGUe6hp6a+WWsu5EM63zWSIV/N7V2Ebyj5YjUPG4SVnCOZL4dscgxeEx9dJaaN2u0cFEA0Q3VUpeVweGMKxR8SXzSk6olYOc8bZ//4bj1ee2347IPIRJvufW/NnVdAhTQwBraMjtQvn8/ZurIMXdo3Jb2e/25aVsIX70DDeGDTAf/Y6knNdwONpPX0Hwe/tS28sD4tDGe/sbE0imtrPkzzUhvD/XTEfA4BtciDrWM6Ne8yeMKCvQUAAZivW44v+aYH0j6zNAbzOgGPPn30+HlXE27g2za7NvedDHrscGgQDxyeXqTPA3TeIsqQqwUp7L8V84yctk2i33NRnYzKfwiPGtR5ESMk4IrJrDDs4NSebXq+8O709QlrXs8P3MF/ncHzey2BUGt0YQqzm+FDr+tyGSKmyi7D0n7FMPvRU2ZcH69BPDBxWpmThpWzS63EDCXd3LPFe1lJt7xfShW4pCpzojk02lMQgWpfysgBiLRxdy/r/WifV9/7avsVAJ8gaxlPqRG3/SBh1T0XESXWBsKDhd3xChvfXuWiGUkhzRt/GL4ekIBZkylpCNZeS4kni1+7ax+oKFJAi/O+vHV9Vvpt89EmmFtMtV0FQyvh3yYMYo/Nm/L0490GvT9l5aX4/8TxmTYEStvefQA85/NuFIcA34J5a+vw9L6PL3zYvkRMnYT+HUx5Z89n67J01gSgDcHa6mtIFiXz+n5SollAlI+jPn1CiQmbHEYSQs2hq8lBxAPGfUQcnls+4IH2/YdNXXsCX0oLQRlaEJjQcO6lh36GDDnX/zPQOuKaY1YtnL3hzDKzfS7n00ekMAufXbzsQOCXzF3aMH/tugwcFO1TRxdh4AglwI8OjyoJ3JaHQWek+U1RhxSKtldI9LP6d+7S/51p3+dZq2Cge1EalbWMn+hQu5anIfLFzw/uw6cjWkbIGCZ/ha+ymGCDvXt90CHQKxGBncsJaRDW1zZp2J7vT9wu9ywrQgpZXMyW7S0JE/3PGp1Vskp3GvRW9ICiOUPaP/T0mNk/HI0TKaZMFP+Mhkoj3SHcA7cNOgxIKHrGPcRETGsmJaYqWXDJy6BE4OlMRAOFWVhEibxCKerAimrIOh2qtBBvv3X0WZj2xfo8BttfPAGRmfXVyXNuBPOWJpWJIgmY53nA48TprRzwWIc+Qz5ZeiKovFR8K8QCJgISgljx8LAE/h6Zs/3Hgiswi+m4TkRWY8jQsRzD58dMjGUuqySX2rAaY7Q9IOsrGTEmF56AM6dOSdDFUwuMkJn9yCwglhRQG/jWWMgHxmSXD279QO/35yw/XBpnhqrrsbRvUK5KglVr6Q/NhnrgaC1gV7uj2gWp6jW2N9RqVXsr6iu01eWsUTJ9DotNJKKQXg6VQZJCo3uXLgkMe4Unon9Gm9545IE+7381/4BvrxChD8uqtKVseRJmhM5qM+PWL9PAk/iQ0aJHKbKK4H8Kq7IspEL3/Ln9O1ImHWaY44DjaHAVCgvAOwtPOldQCFuGUqmNo9s/0vvtj+dsz8Tv9iNp6UBXgtBIkIHkyAIm+86d8zA1oyuAKhjSH1xMA+JP2tXYW6nRo9at7DX4kkADaUMxx3OC4UOliPzIaJ6wLrZmeI9OvYdNXXagiMYSNaRG2Wj4jbkMsyUJSIzuEf93JQ6OkFoE4nCb1UidWir1Z7CCdVdk9DdevlS4+uHPCGSY9pS1p+9rTDoGg5mgRXaPe/zOtm9Nn7sZ/VMZvCfGrrbRbhiljFXX0Fi6cIfrMz067MDfUf9jZWBW3UMCrKiE5n8Oq7FQ4e3P8JHH3LwPshxTKyAYiZAZiiZjdk14pkXPgSP/ub04BoOqgBZJYYUAurOlESMrez4mTIFOOHChe+vVYDMJi9DJ/He7gIexQI38M1gtidhvz09zCRy/BTNHGGmNMpnH6ZPum9KlRc/BH8zbe9n6GmJiIerj0Iu9gEljeTSKRLUizAJJwZ5mPY4JrKZwBDjyxi99l2BFixFYPy18DR+whoGXJgTSFNy0AEymTGvUxGjPX6b1urvTwDEL916OqiMRXcaqQV2RaK23WwrHMUZCRwXDMPccbdXlUlzH2MfTUbSlqWffYepHWdfiV7y9gaFTkgJmdtlpu2Qhvnruy453t37t0y83neP1qg0UdzOeoVmmArm86ZDi6tjVqmxGF2jIUStnxfzKVL8pEg4//kEWWcCkF7Vt2vaV2cu3HnOsYZioe+Q00Skp3EKGDjT330eW6epUzCC/+8LcYI35NWIThn0wfvDSpLm4oP/99/UdvfinY2E5TkYx86prN6JtqvRQqvJM2tD37lmXhUy1vQWsv7swJ1jL+VWIY0ePHsvXu556qNuIxWv2xjhpKMoJDb9knaZFvwzSRrqv3Y1GjKriXUbAp7TlOcFawa9GxobrekP/I8WW3ZGsjFGaZQIuBav7VoYZR/GTJn/Y/bvSxFTTrQrh8qBJLEdYy/kVSj0oK31w4GPfmcClBIEalJq2SMUTZOTV4QPAU5EooKkmrXdTqURQ5a8YD1s75QmZC6wV/CoUYxGfPeTozubPlqCeKqOWcxT6q+DClt+mLn9lIsHzm/XZjlpGqrASqxaazG+FL+TGrhUki3UctJsgYWv7VwtQ0mUlCVESEmld5BoYI/yyc0EeVnl7WrQptY+of9NGoKZwyDCgKidYKw8qRPKRbxH6xfuanCZMlobSY3XzqvCEoqGxJcuR21/OqxG6Ena03G48yCnWQJhlvQ/jDzg1+L6NhhehTKdldYs4iupVSt8t/vG2MZeB1YgG+LYpUzKnWG2+fmFUCCVEJstG376IqJAyxS/TOnKAh7WMASwRl/3t00DwqEY4lHwwAjzNcomVa+M++BU6XSBDiD697SNqmMp6UR2OZqwiwVjk4++fjxV5subp+9rvU4EiucSKynJ1582YYYmEMo//eM9kxrM0rHPwDOYrAokh//sbINqwmph++luJIWUml1hRtg95uwh0SZT1GMrObXd0K1Jau3WBVRKLtdMTW+9TIc94UMOu5IsnPGBluY0tHbWZolFpoOokNont7vrMcduPquNdDuaoVNeb9gMRSkhew67H+/+ghStYbu26v+dKNIMt8eNZCVHYtvl5mxIciV819IDwtR+orOQpcJ586ojUccGrq+yqAtvEVrDu5hKsx6jOJVajxw8rBFqFibtwufODR8FHIRZ6iv3+Zlo4kQxLNKRO3PXUZagxyY6ZSjNjyIxuSlNNcoqVwWNTMTSqbqmzESRG3bgJb5Ik2qnBs7ooUr7kSXn2jrcumFRNt0YBh2N0/tmFtqjlOfUB+WuzFUBNVYM1ZKoMghl3fBhGRF8JTY3wx5eoI+ms2ydnIOVfZaCYRq2x6Y4LBp1YiVxihUm9zkpeLTy5ueJph834+3jXlPrVz1CJJNIuIVp8cffMIoNFt6npU3bc6YxWKCtMA6dH6sTaZQJW8tJUXdUNdIkLPO+u5xJKBjX4QHORADGx2Q+RUQ5T5Hf/Ry0YoVnPDZ5glwoYnVN+PfPwKgzc6ltiCg98o4i+2ObRs6B+Hxw6zQwhI/9tBfVUUugadT9iJZhetrY9gZUvx0jMFVY7RjO7HpdciyrxhoIU75+lRlx4puUesA2Wf7GNlEWZV+8+xI2dxWY1QssovFQEy+5QODaZOta31BcrERA5yoEeHwvbzAlEtcNB3Ku8pNID7t6BkZQNDKoGPIsbgjLBSz537+5YqANcZYh1SLRy33sRL2HbAjnxAWHn7Q0tfWIexhO7imOJKJMZ+df9WM0orKjCUGBlqjIKkk8+chJqFXuaogSCQy13wR84aveByFZ+S7rvtOu9aj6+oSgWsx/fNMY3WQwnrpljJzPg1J29CuKZmKsfKjDoTt/fonOJ1ZgIQwNefj1jq0FeQ3tkaOhQw+c3m3ZFmRQiQEpwQth4y5iUSQjt1wZGYsmVmDwAconVFqrU+G2/wCIGbVwjv6hSVN1pED/fOiRDuAlFCdWZ1I5733Kzkp0RtcpbWw0e67oxyiVWRKgJbO60A3z0BSqvMpoyzBBXnGvR4QKAj7XtxXDVzR85QBOK1lqKKzuduemmQpNLrJj9sIR/fXAKsGJRNX0gUCazccqUCUvdRI9b9gFLydAZ+ZeV1BUmylLFTe1mdT7rGuTUB4BRzNutPzdIn6GoSZQ6oz4aeLoo+e70qOyNDuu0idxhf52Lg+D5Rl+jzsUC9niv+drLKVYTSPen59eXx9lVbu0WNv8OVdjh+45COPre5V66b+sjVDt2mularKl82NSyzOTUX+PW9LsvFtRqdvF9xzNBVhXdvBgid0arD5r9+zEw6bqLaO1ObafB5BYrONBxRK3X5Gb6I6c11/z+mUzL6MP/edtRwkm2rj6K1S3PToQ/dtSeC6hzqf0yqC2gNV17Vz5cDvKaHEpQOHd70//39JVLxJC66jAGB1uctSV5LrHqCGb0PStrE+6OFM0XSCbXP3lKO1tbTkwUt+56JiHDunrHSn/X1tiFbTnEKrgxT4+pfZJMR7qg80/e/mc2g7/45jEXA0g91vxQtu7cWdp/DNNhbv1VwMl2y64RA66AstmTl2I1Ou/m+RGYMi81pMPSurvHJ5rtoQ1rZdaJFUHO6Jl3jcFE1eyFbgTJj/6+QxMUAxLKRty5nEPlJNDviK58HgnMmmZuZbc8V1hRt3T/IMNUbRcl1KRtdZ9+9ZafONeBnZEH9k2TcR4EgqQVKBSLqlpKKiyvBHpUyWsfMpC5tSswt+N3ktQ6sy9OuJpdMCXv/GU/y0gs9Q3IAJxld41OQCnqLIUJRFBWFe9KmXhNzN5HtthpnNxi5at77kRVUBvWIifFTFT6yC0nSjiPAmX7rQILqG3N2hSgRPXL5warhkVTrAjQK9SyZmUQT0jmEKuCV95MGEZru6guiCL5a9NeF4kUBRHWq6gfUIBTfeipDjtAYtqPM3Pl2w2zJxAdfNbfTmo3rJdZJ1bV9gustWttOBkG4pdW7a5AIAvDDJoMcdoKK2vKejQ/CpHSHAuLqkkijKYQsB680G0JR62pc8qvsKvHRqCq1kkdwtWeWz7JKJ9EMsu1QsWqNApJnSjyRjXdnJF2dQ0a2lRiVR6oyKxpcpE3sItVD6zD37piBFO1OhZbeNMHvsc0atuICjetUGDRjJQlHIrfu2+DXbAhqxfnGCFDpIJgdDd0ViZUbvzVxJrO8Mc+BmY8ejXitSLBmfuP+TpidpmTqyCF2toPjA6VJ30s++fd98+LoIOoPIZsRxPLXJmGgi4LbflmBM8JVm6XNGj280M/os/qGjwgIxzaQDvT/jYPiPCEqWb5ihkxu2gz2N10RLFx06A15mriGW1XDiuz98aEnWkwOeIBLeKlMp8/f7ZG6rFHGXEyDE6+/vAaLrB8FTVdz1pRBfse67LXLr4TkS1ndBB3BIOp7UJ8Okx5OclbdmZYKKp7fWStdRUoDjdO8bNtNpjzSUWvKu3i/CHO9+p+ARwWh5WxjUxm4NKTM+0FtcxNjlWSK0PgeCuUrlTzmnVWWuorTzy+R+lkgPmqRpCouE2D/g6Xujy0Xye5/d2W7MpTsPu+K7GbKJ0bH1BYEbgw8alfgQbK1Hh+L9KHWrUrgIzLTCGVwe/9mdsJZXyfcWh68O3fG2KTLXGNnSZm37SyT/vHgF6VB3B8IvXcWIrBepWLCrO29QsX7RRGMjJBzT5ARbBJHgpJ32qyJAROUClouxun5PU3rQP8QXatiRVTuJJw+olF8ZLbmsGlFt02zQPOUWS5KlXzaVT5Wg2ZoZlCI7/+x4QMYBEeaTuDf6TNHg3xijitcoGVCEFD+LbrLvCpRW6XE8WMFPcoQc7/+/s+cCWMLySSeo2+tlLlvVqV0MZXsOnWsQkcKnRYrItXtMKLaMsBMif1lpQEA2rQa17VvSWNaUbaCMn8s+ksiZxLaX197uBtT50HZvckgPP6G3+sJqzVX4MQyvgLU6ri3sQdX41RVMQSA2+cLyDNoN5zaEZnOrbIR6jphMm/Zz2w3GINDFnVa3uVnXWMN+7yFz/z4FoNLMTRre/Ev8oot/sdWwnlwJc2+YP6qtZcAHjZZ/u5lWNstwlw24NRcLzdo+dQX+EfxKt3bJhQZ5++dSd3hDvjWSohl1hRdwrW/qMqgWRrk7hLTc/2bHFChOhwnES83rwjqevzz++ZRfjxvquSYHKKFTPR5mfW/SuNWQLPe6RvmVvClYybhlE9DWv8FJ4pv7x5rL/+b0wxnUusduHUW0NLfrNdwHKW5qs79D9gixTihgblTX2x2iW7hrJgRdM3R3XTkIXcYpW88xjUlwgxZmxDfA3e+lYjw/ItOsLuBrmq/LRLO8vVYdzXLF+or8pU3GzdecN/X0CCMBPF/QP7D8aR+7IVa6EkvmqXnzdon7yJzJ52a7mvGNOYJzGLZRMgZ940PYFXZrpW4SmE3UlqOwJYIFjhbzBPVJycPLJm9rAnOl9kG2ds2rTxnLTrHuUvySRPjV1kqAh8l2cYVeTkJeE3BCvG/aiXikCgmjOS00hkI3Am3f9lSsSzp7UKTzemMawlDUfUmlV2wop/3TRrUNtWLXocABKtvv3XDX07JKkOU7v2KEG+u3G+TkoIC1Vk91MkDu5u0B5ppuDxsVjpR1IH1C7S80Ty9b+siXeJcruJo5braBSl8Q5dVOpRRWczeWTDknHPNm0+ZJ31Uz/QB28DOPVvazEBrntGUrJ76ORFqJEJE/TXE17pflg/0G2QXU1J+zngEAwjx+5z8GTRwGYHUAFoabeq1SqSOEPTUFQoMa0hzuMb5rzZtVWrYSsyKDKYbW8I/9C9J4582+q4zMjd7yZM4Yrjr8wC45b6hs7on13ek5/9cHmD8hZMfTHfkBCdDxVTROHQk+3ypKlYCWCukUzRWysWBDhH1swb3uHm5iN/duKNLahXpKRZEeT9n0nvPjXSJZCa+C1LzZmz/5VJfjlP5o3aeHGD486e0iCsqtNojMZMgKzq4YUOdm+Tz1NSWKGHirZWqtI8sjuIITq9dubYV598eNB3BXYZv0bhYyQjhPu+gIP/AFjdaj5RBUOm6eOvfTbg1r5H7HIebg6/vS1/O6RHjGwQ1jMdvsYY8TgRkOTww939EkANz1JjFz5de4k2O7Vh/kcvtHzw1cX5JbG1pJ2yV+UEpnQER5qAvPh6DwhLZk4S59Pu930/KA5LMQ7FqeEz90QymD25XliRTKXtSy7rsw2Ey9DHJFMbmr9w1s6euyI2akVVHS84NuVKvJIYgos7F3/04sN3dZ9+obyDwd3QNmLRqDJepE6wPFh5+7687+/YoAjsGIaVmyqc9Q0cGHsCqJuZNbIMzNFJ++qFlYbG7nCBt18shtCjRJMA5t88rpJElCwv6DBDSCFkrO6VXbBrX7uyfenHr3Zo9cz0E7XpU8O1p+ji4Z9PmXbAGFfmDwndAp38ucQcfGmNJ+HKin0owDdMrFfeMpIqu00l3Wa2kSTtZZiK5t3+arrqUYi0IEX8yQvGFjrllGBKdi/8eHCHZv2mH7mWjtbcBI6xrTgjkNkMP3XoCgmZ1mGCRJfzvz9+ilJdtOXXemFVyoo9BWv77Wc06UoJpWPvnP7bpoPhYUg4xopWlR3k4u2LpgzteH/HCRXNel3rmjtEaXwOEj1BhcjbIjyesLP+3HfKPLGz/YbIRCRZALJeWDXnVgCOH3LOtkhCVfryX1Zh2S2ruN7KGsm1Kd/8J0r2Lv1kUIeWXT/Y7sUdEIw7xnVtc8Y6Qj5ArNny7rtyPSQOkKEQ6csKowGow12oY21ZJVZtBMVY8R77BIsp5kLxs52OoRmq6ipp9bYoX/euSw78OOGVzi3avLuv/DEY5ZjUuOfXLj1MpAznUtuC1tjPydDUAcVJCmgEJKHCBOZlyuplV0xJHG23pcsCtJnjHO3e7Ci4QcWHP5SjLW8YOcd/+Hhwt4c7Dd/g28lVY0K7NZe5vk2/staJK223UqMPcRvAdkl82k4fa9elbpYYzmy330ma+mlCZUt3GNv3IrBA7m726FngVhb+i6W8Q4snj3i+81PvLD9VETFMcoJWsh8vgveT1KnFssau1TK2e2C7WTwgNI1pW4uAZVxWpgiGANNhHUuAq3xAWU8Pu3yEZErWNembjRdjxOvuy2/PTq6aMvSZDl2GLr0gK1hMx7v8YlqwnTW4xmpWJEMEoyWmhJhK7IclcNt90MGleELM7qkzdZSO1f6K3K12tluEvy95YNBly/3ShoxFGuatmfLOC20e6r/gIjTiUeUDwu6h/bzfryCXPDz+CuOSRXFgBb+umPnOsx0e7Tv3vHVacz1gtZu/YNBQo2bcOTXCWjXOUqeXzRjTp3WrAfPyK07RcB1gtc4jfhmwyh9754q42afPr//q/f7tH+g+5UhUngoIylN1PWANQ9TRk146+P4dy/CvCxtnjHv3uce7TjoSe7tts8VtIc30dYDVMMXhzY4DOp6M1n83rne3Tr0n/WxXJmHqRRUgZOBjFhbcl9cDVtQtZZ3+x//qM23w8107v/mjW07gPAoIj5uQCgsj2qjuWoXVypEZ/+W/dnyx63vrzlfiV8JOGOC/iLBbRs11wgP2wwAWPTdxa5FNtzpTRcpURoGI0jT+RAukfHUdYJVuYOV8oFBBYFKv+oAwzIceK6WgKLOJqjHNWoVVYEXkhYxAma8dZrctlx9YzHjAaKB0SOP66TrACsk5e4XdyORkCtJ8+feVzRqxbmj/XcxPB5pxrMHUdZG3tjX5DGs0EpQcOZgxLzx2puLlwk/f6ddmD83b6WKIhVxfD1jV2laDSkLHwLwvUTptfulgxevnEgZaLITDH+fZea/GZNdqrCeXbOk1zdLBuCUg4KeXD1T6QLrUG7IJYPhqlJ6BaFy7avRSJeHTF4916mc3QL6+BeNp3RtHsFq0/BQRWLGk0MDYqT6W5bpx/dUEgUiL1Phx695rvZJHqwYe1ISvHnxIE6kizhhcmHMWqWvhmydUmhEKjYmVB4x5sG6BANJyLIRrph3HwnrN6HxrVV9QfmG1b85n5dxPziimItaoWCkHEaaHTZbGGXjfGigb/i0nMOPBbeBMWysiKOz26PARa5MwaQm3JVnj+iuWKTRIL/0xIle2j1mWhQHTiUuXv3/ETY1871IgL73Z95XeqLRHbIEoYCYUjYqVJSPlAAmJnSnz3WM/XZZp21uAs5sLharYhXt0Yan07Cd7NKoeENLnMuGDG4HjIi2ZwkNp7mDNzo5lIc3xZULDov1J+1/NGjfHBgQE14pnUszuY1EUClMkSTkloKIgoigGhVdAuEL2El6jJoMbsKjnzPaaOLXT+nFFFXKwnQceGsntinijedxm0OL60C7/CY7/TFj/P5mv7331HdeMAAAAAElFTkSuQmCC)
By mid point formula, If (x, y) is the midpoint of the line joining points A(x1, y1) and B(x2, y2) Then,
![](data:image/png;base64,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)
If O is the mid-point of AC, then the coordinates of O are:
(
) = (
, 4)
If O is the mid-point of BD, then the coordinates of O are:
(
,
) = (
,
)
Since both the coordinates are of the same point O
Comparing the x coordinates we get,
![](data:image/png;base64,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)
x + 1 = 7
x = 6
And,
Comparing the y coordinates we get,
= 4
5 + y = 8
y = 3
Hence, x = 6 and y = 3.
Question 7.Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4)
Answer:![](data:image/png;base64,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)
For points A(x1, y1) and B(x2, y2), the midpoints (x, y) is given by
![](data:image/png;base64,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)
Let the coordinates of point A be (x, y)
Mid-point of AB is (2, - 3), which is the center of circle and point B is (1, 4)
Therefore,
![](data:image/png;base64,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)
Therefore, the coordinates
Question 8.If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that
and P lies on the line segment AB
Answer:To find: The coordinates of P
Given: Points A(-2, -2) and B(2, -4) and ratio AP:AB = 3:7
The coordinates of point A and B are ( - 2, - 2) and (2, - 4) respectively
AP =
AB
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)
Therefore, AP: PB = 3:4
Point P divides the line segment AB in the ratio 3:4
By section formula,
If a point divides the point (x 1, y 1) and (x 2, y 2) in the ratio m:n
then,
![](data:image/png;base64,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)
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hVor7eBOITiPEexugjvmTu0QRMoO8EitaO1m2hWAbpLqE+tkr46YyivJI6Q6ok9aq1mrqpVreMayXhV/qnJoakvgpUj1i1s5v0k5rBvOctM0j7Mk6PwwRMwARMwARMoB8EWreFZg3SZVu585Cotvm9gaNntrQfH2rDq9b0Yzsw5BThr/KkRwGvbDiXKoOqM7FT2bJviMu3m4AJmIAJmIAJjIxA67bQrEGqJPZZUFPZcpnyGm4ZDL/ZVEqKyPp6qBUvD6X+nLLtH0qVKv3UGQ0enG39y9OqpP9NmnK7KnWUvLd1219C9gBlQqjb6sxz3Wf5PhMwARMwARMwgWETiGkLzSVRlPbpsoKE8kUdyAspT6hqxhelIdovROwrF6kSVhfl/lSw0NuAH4drm6QzysYomc4BlHf0fg2T8q8Rat0rlZXq3jdpOsqwfsMoe/FRwYKqOWJnx52lfSo7z01k9r0mYAL1CLSxNtYbie8yAROYOoGYtlApg1QXKTJehpzqt88zDlcFdgu16VWRaV5FJ51VVH3760Jwkcp15tsLZkqU6pkxks+vE1JPaVzy4P69gSbpKIIMN43t4gb99O3WMvPctzF7PMMhoHdQhSnc6hNoY22sPxrfaQJxCXiNiMuz7d6S2EL5JO0y4M4NW+1X5CRUaSxt5SvJvIxSnTlVnlHlxfzJzLWrhO1yBTTdGHJ/yrhVpLsMIZ0rzdomIVeojNb3A8c0oPpyYDtgXeDOIbjqFyHq/6AaOUg1FKXA0r2qPlU1h2kDUVq/ddE8t/7wkT9AHuhnAnpf9C4o7+tdAAX8fW7ksks8ldl9Z3gXxxAE2NWUxVwbu5LBzy0m4DXCa8TQ3o0ktlDeIM3Kf34g/ICmgrZRCBr6cKoHlniOFo0zga+FYwklbhnMJV3N82AA1Ryo3icVYfhyKF+bdaNUap8IuwqH1uy77G06v63iFgcA15a9KdJ12tY5D5B+jSUrRSQ0tbvp49pYWxjfuKJSn9cIrxFDehWS2UJFZSyfEX7MtHV/QyJqO4Z8pTG27GMN+f7AWcDWwJWxOu1RP13Mc4/Eb2Uo8opKh08CXjWTXUJG4iUhfdgDAXnu22o6e3g+sC1wVVsPmdPvC4PR/TsbpNHI93FtjCbcBDvyGgFvALxGDEf5k9lCRQapvBvKN3UKcGICZqqmdEgo7Xl9gueVeYS+CCS7jAsdJRhjSz3PY2SYlylLN6bjLpvNFIXQ1r3SkOnohz70Zo+txObSlUEqeTcGdHRmbRukUaa1j2tjFMEm3InXCK8RQ1L/pLZQkUEqWDonKoNUXjSVE22z7R08Rjq72pemc7E7h+wAOgc71pZynsfKcFYuGZ7PD4F+s/osA00BfjrbrPRfv2oRRhcG6eoh3+8RYcveBmmcCe7j2hhHsun24jVi5bEerxHDeAeS2kLzDFKhUnDCa4C9Wiz/uVbYWjy9R3MjuQ8Mqa+u7tG42hpKinlua+xD6VfnKS8MQYHayi9KgRZLli4MUkWEfyl8WH7ePzZRprKPa2MUwdxJIQGvEVaMvhFIbgstMkgFR+ddlEP04A6qLXUxOcocsA9wGHBNFwPo6JlTm+eUmFUI4TMh1+7LEmRrSG2QSne0cH08QLVBmlK7/KwxEPAaMYZZHJcMndhCywzScSG2NCaQhoC25XYFFCGtYy8fBQ5P9FGX0iDVOWSV5lU6uCzfrw3SNDrmpwybgNcIZ+IYtga3MHobpC1AdZcmMENAW6/yuGtLTlHoTcq+lgGb0iB9NvDN4P3NxmaDtMws+RoT+DcBrxHWBhOAFTnR3EzABNoloPycqvSlBPlKI/bTBo9bD3hFKPxQ1I0CjJSY/2RgXtYKnWF974Iqa2WGp4h6yZLPxGGDtAw9X2MC/0nAa4Q1YvIEbJBOXgUMIBGBd4eE2McBezZ4poxapVbSdnldg1SZI5TO7Dc1x6Htxv3DVn0+V7EN0ppQfdvkCXiNmLwKTBuADdJpz7+lj0vg0cD2gCqd5VM7KVju6JD+6eGhrG7cp6/sLcWWvTyjyh38ywIBdgilhc8G/hnKBf+gDUHdpwkMkIDXCPAaMUDFTTFkG6QpKPsZUyCwWqjGtGnwHO6XE1oR9tom/0bY6m6rznsKg3TefGYFAPTvLh06Ba23jFUIeI0ArxFVNGZi19ogndiEW9zWCKiqjip7qTSo8nJ+OvekY0Ju27cDr25tFGk8pDZIW5xAdz1aAl4jbJCOVrljCGaDNAZF92ECKwkomGhN4PgcEFVoUqWmvwLaslMd57Zalx7S24Soe6WAeliLxxLaYud+TaBtAl4jVmbm8BrRtqYNsH8bpAOcNA+5twT0PqmQxIOBM4BLgQ2AQ0MQ0h7Az1oefRcG6T2A1wNK8P2gIN8lwLXAm4HLW5bZ3ZvAUAh4jfAaMRRdTT5OG6TJkfuBEyAgL6kO7m8WKn5dAHwrBPm0LX4XBmnbMrl/ExgbAa8RY5tRy9OYgA3SxgjdgQn0ioAN0l5NhwdjAr0j4DWid1PiAYmADVLrgQmMi4DOcaoy1EHAdeMSzdKYgAlEIOA1IgJEdxGfgA3S+EzdowmYgAmYgAmYgAmYQAUCNkgrwPKlJmACJmACJmACJmAC8QnYII3P1D2agAmYgAmYgAmYgAlUIGCDtAIsX2oCJmACJmACJmACJhCfgA3S+EzdowmYgAmYgAmYgAmYQAUCNkgrwPKlJmACJmACJmACJmAC8QnYII3P1D2agAmYgAmYgAmYgAlUIGCDtAIsX2oCJmACJmACJmACJhCfgA3S+EzdowmYgAmYgAmYgAmYQAUCNkgrwPKlJmACJmACJmACJmAC8QnYII3P1D2agAmYgAmYgAmYgAlUIGCDtAIsX2oCJmACJmACJmACJhCfgA3S+EzdowmYgAmYgAmYgAmYQAUCNkgrwPKlJmACJmACJmACJmAC8QnYII3P1D2agAmYgAmYgAmYgAlUIGCDtAIsX2oCJmACJmACJmACJhCfgA3S+EzdowmYgAmYgAmYgAmYQAUCNkgrwPKlJmACJmACJmACJmAC8QnYII3P1D2agAmYgAmYgAmYgAlUIGCDtAIsX2oCJmACJmACJmACJhCfgA3S+EzdowmYgAmYgAmYgAmYQAUCNkgrwPKljQncEngOsA1wV+COwE+BdwPfbtx7Nx1UlemBwHOBa4B/AbcHjgN+1M3w/VQTMAETMAET6J6ADdLu52AqI5DhdlAwPD8TjLFbA4cBLwH2A44ZGIyqMj0SOBzYCfhDkFWG+anAq4CLBia/h2sCJmACJmACUQjYII2C0Z2UILAtsCFwfO7a1YALgAcAWwGXleirL5dUkWkt4GLgYODTOQGeGf5e8l/XF+E8DhMwARMwARNIRcAGaSrSfo62pWWQvhb4Rg7H/sARwDuAAweEqopMTwM+CtwX+HVOxo3Clv3OgLzHbiZgAiZgAiYwKQI2SCc13Z0KeyawI3AssHduJE8N29byHMooG0qrItPHgK0BnSG9Nifg7YDvAecCew5FeI/TBEzABEzABGIRsEEai6T7WUZgi2BsHQX8IHfxrsAJwYOoPw+llZVpD+CrgLbtdc8NOQFvA3wX+D3waOCfQwHgcZqACZiACZhADAI2SGNQdB9NCEgHTwF2AbStrQCfobe8TJ8NBufVwCOAm+YYpIq63xz429ABePwmYAImYAImUIWADdIqtHxtGwQ2CWdKvxS2629s4yGJ+8zLtEbYkv/tHIN0lRBhrxRQm9kgTTxbfpwJmIAJmEDnBGyQdj4Fkx7ArYCPh0CfHYDfjYBGkUx3Ai4FfmWDdAQzbBFMwARMwASiE1hmkCoVz24hMjq/zRh9MD3o8O7AS4FDCgJPejC81oawaJ4VAf5iYJmuzBvcJcAn5vyjcm8+D3giIO9hqpZaptsGD6nOiC7aspf8RR7SqeplKn3wc0zABEzABDomsMjIeDigdDyKiNbZt3xbFXgKoOTmV4RAjPXD/38xeIN0j36MnwT8I/ydAjjWDUEeP48gv/JYahxKUi4PlM7hZeM4H7iy4BnKH6mE5Lpe26XrAecAVwFbBrlfNEfuCEPuVRfL5vkeIXF9XYP0m+GMaF7oJ4cgJ33w/CkxkdQyrQ58K8j4EOD6nLxZUJP+/qEFQU+6fGp6mVgl/DgTMAETMIEuCcwzMu4ZtlIVZFJk0GnMMkSfAMjbpNySMjK/H8pAKn1PZmSsDci4e1P4IT4pnJc7L0QVN5VfP/bysN0rJBdXCh1tA58FKJikyNhR6Urlvbx/uPbzgFL4ZOl4lHpIsu8OjOFM4zzGZea56fwU3f8oQMngXw38deYClRJNbZzGkm+RTH8GpGPydMoDOitz9tGmKPufANuHj6qicU1FL2PNifsxARMwARMYCIEig1SG5umhos68rda8eK8D3gy8D3h5gez3CQbgPsBvWmRzYtgCfj3wlgXPkYwfCYnYM8/V7OXytqovJXB/T4vj7bLrOvMcY7wyyJ4NvCFn7Gs8Oi6huvZDa2VkehuwF3C/gg8xeehljL4zcJkn/xT0cmhz7/GagAmYgAlEIFBkkD4nGJXyIpb1DsrT9u3g+dGPc1anW0NcJ3guZYAUbf1HEOPmLrYD5Hn9DqCt6Hy+R12ooJMDgLNDKp55z980eFmVF/LymIPsSV915rnp0OVNl+f5vcDfc53dG3gs8KGmD0l8f1mZHgR8HZAnNV+pSn8nvZXOylO6qI1dLxNPnx9nAiZgAibQBwJ5g1ReKiXwlqdTHsSyTf1om/xZgAJVMi+Xts/lOT000vb8svGsCejMosozPhK4sOAGHR/4WTAAFvUnb5S28RUdra3lMbW689yEgT5M9BFw53CeON+XUh49HfhCk4ckvreKTNInlRpVrXrtIuiss5renQ+GDyVVaVqWFH/Mepl4+vw4EzABEzCBvhDIG6QqbSijQVHX+Xrby8Ysj6qCmVQCUZ4e9S1j9MgQ9LTs/lj//tZwplU/8jI+Z5tKVyrISsZzmfZcQNv/qq6TL/dY5v6+XtNknuvKpNKZ8srOawp609GOGIFudcdY9b6qMkn3jgH+N3z06R15ZdjG13GFa0oOYKx6WVJ8X2YCJmACJjA2AnmD9O3AVmHrdJmnJs8i87opSlhR7+pHXtYfJYamWuFKNaRjA/qzAkrUtC2qCGdtF2feqWVD2zgEaikq/yvLLh7QvzeZ5wGJ2cuh6p2THkqnZITLI1x0jnnR4Meql72cMA/KBEzABEygfQKzBqm2AlUtR+cv5a2p01SzW9uSOnOptD7qK3XTGVFFND8mbAF/EtAZV3mVDpuzXTxvjErHoyMAqrMuI65J07g2aJDPU8+WIa1UVTJk6rYY81z32b4vDoGYehlnRO7FBEzABEzABBoQmDVIs+Td7wrb7HW6vUMIylD6HnmBUntHszHrLN6x4fiB/rxvSDuVT7ezTEbxkQdLSdt1PrZJUzDKp8JZwbr9yCBVUJCORdRtMea57rN9XxwCMfUyzojciwmYgAmYgAk0IDBrkCpHos7vyZN4co0+1Zcq+ii/pM6TyqPYVTDQ3UIwkrySpwaDtG6Ev4xIlX58XIWt/hr4kt2ybJ7fmGwk5R4UYzwx+ig32nauKhr/2PSyHXLu1QRMwARMYBAEZg1SefDkedsJOK3G6HcF/ha26XUm7o/A5glSPRUNVXJdADwYeBjwwxryZLdoy3/DOSUfG3Tb2a3L5rlvxluM8cToo7MJA4rGPza97JKvn20CJmACJtAxgVgG6S6A0vYoh6TOKMorqTOkqlOuSOTUTWORca0k/Er/dFODAcgTpVKTRTXIG3Tb2a3LDNLOBuYHVyIwNr2sJLwvNgETMAETGBeBGFv2OwBKan70zJb240NteOU0VbLzJgZhHeKK8L8IOCqk1anTR3aPyqDqTOxUtuybsPK96QiMTS/TkfOTTMAETMAEekdg1iBVEnt5FRXUVLZcpryGWwbDbzaVkqKAVZVGteLlodSfU7b9Q6lSpZ86o8GDsyoOkCQAAAUkSURBVK1/eVqbBjUpt6tSR8l7W7f9JWQPaJK9oM481x2v72uHQEy9bGeE7tUETMAETMAEKhAoSvt0WUFC+aIu5YWUJ1Q144vSEO0XjFvlIt19TkCQgoVU4/vH4dom6YyyMUqmc0LeUdUNv6ICj/yla4QckUpl9Y4G/ehWHWVYv2GUvfioYEHVHLGzQ8/SPpWd54ZiN769DR1pPKiOO4iplx2L4sebgAmYgAmYwMpqSrNNkfFKIK/67fOMw1WB3QDVpldFpnkVnXRWUfXtVSpRwUUq15lvL5gpUapnxkg+r3KOqgeuccmDm6+ZXmXedRRBhpvGdnGVG3t+bZl5riKC9EiGowLZYrc2dKTJGNuUtey4xqqXZeX3dSZgAiZgAiMjkDdIZcCdG7ba855F1YfXVr6SzMsoVfog5RlVXsyfzHBZJWyXK6DpRkC5P2XcKtJdhpDOlWZtk5ArVEbr+0NZxbqIVR98O2DdUC9dnsBfhKj/g8I4qvatFFi6V9WnquYwrfqslNcvmuc641g96I2yKyxKryWjXqVpq7SYOlLlufOubVPWsuMbq16Wld/XmYAJmIAJjIxA3iDNyn9+IETMpxJ3oxA09OFUDyzxHBm0ZwJfC8cSStwymEtiz/N64aNkzQUErgeeGAoN1AHVFx1JIesiPmPWyzp64XtMwARMwARGQCBvkEqkZwAHhK37GxLJuGPwrMXYso81ZAVknQVsDVwZq9Me9RNznnV042XAeXPOtyqgS4bUaxoUF+iLjqSQdZGajF0ve/SKeCgmYAImYAKpCBQZpPKeKcfhKcCJCQaiakqHhNKe8qL1ocl4kuwykHWUYIwt5jwrA4G244vOCSsAR4FrMkbrHnvok460Lesy7+jY9XKM75plMgETMAETWEKgyCDVLTonKoNUXjSVE22z7R3Oeursal+azsXuHLID6BzsWFuseVYu2i8CeY+69EtncFUoQcFhdVufdKRtWRcxmope1tUT32cCJmACJjBQAvMMUomzRfBq7dVi+c+1gG2B03vET3IfGFJfLQrQ6dGQGw2lzXneHtgAOL7BCPuoI0XixJB1Eaap6WUDlfGtJmACJmACQyOwyCCVLIqsVw7RgzuottQFS2UO2Ac4DLimiwF09Mw25lnVrd4KKPtBk9RbHSGp9Ni2ZZ2qXlaaBF9sAiZgAiYwXALLDNLhSuaRd03g8LCNryIFY29TknXsc2n5TMAETMAEOiBgg7QD6BN45IbhGMY2wP+NXN4pyTryqbR4JmACJmACXRGwQdoV+XE/93WASsv+97jFXCHdlGSdwHRaRBMwARMwgS4I2CDtgvq4n7laSAH1OWD/cYvKlGQd+VRaPBMwARMwgS4J2CDtkv44n70p8D1gX+DIcYp4s1RTknXkU2nxTMAETMAEuiRgg7RL+uN89q7ACcAeQJ9KwbZBe0qytsHPfZqACZiACZjACgI2SK0IsQn8D/ASYCfgtNid96y/KcnaM/QejgmYgAmYwJgI2CAd02z2QxaVnVVFoSkYpFOStR/a5VGYgAmYgAmMkoAN0lFOa6dCqeTs00OE/dmdjqT9h09J1vZp+gkmYAImYAKTJWCDdLJTb8FNwARMwARMwARMoB8EbJD2Yx48ChMwARMwARMwAROYLAEbpJOdegtuAiZgAiZgAiZgAv0gYIO0H/PgUZiACZiACZiACZjAZAnYIJ3s1FtwEzABEzABEzABE+gHARuk/ZgHj8IETMAETMAETMAEJkvg/wH+wjIFbPYl5AAAAABJRU5ErkJggg==)
(-2/7, -20/7) is the point which divides line in the ratio of 3:4.
Question 9.Find the coordinates of the points which divide the line segment joining A(– 2, 2) andB (2, 8) into four equal parts
Answer:It can be observed from the figure that points P, Q, R are dividing the line segment in a ratio 1:3, 1:1, 3:1respectively
![](data:image/png;base64,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)
Coordinates of X = (
)
= (-1,
)
Coordinates of Y = (
)
= (0, 5)
Coordinates of Z = (
)
= (1,
)
Question 10.Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken inorder. [Hint: Area of a rhombus
(product of its diagonals)]
Answer:Let (3, 0), (4, 5), ( - 1, 4) and ( - 2, - 1) are the vertices A, B, C, D of a rhombus ABCD
![](data:image/png;base64,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)
Length of diagonal AC = [(3 + 1)2 + (0 – 4)2]1/2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Length of diagonal BD = [(4 + 2)2 + (5+ 1)2]1/2
= ![](data:image/png;base64,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)
= 6![](data:image/png;base64,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)
Therefore,
Area of rhombus = 1/2 (Product of the length of the diagonals)
Therefore,
Area of rhombus ABCD = 1/2 ×
× 6
= 1/2 × 48
= 24 square units
Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2: 3
Answer:
If (x1, y1) and (x2, y2) are points that are divided in ratio m:n then,
Let D(x, y) be the required point.
Now,
Using the section formula, we get
x = 1
y =
y = 3
Therefore, the point is (1, 3)
Question 2.
Find the coordinates of the points of trisection of the line segment joining (4,–1) and (–2, –3).
Answer:
The points of trisection means that the points which divide the line in three equal parts. From the figure C, and D are these two points.
Let C (x1, y1) and D (x2, y2) are the points of trisection of the line segment joining the given points i.e., BC = CD = DA
Let BC = CD = DA = k
Point C divides the BC and CA as:
BC = k
CA = CD + DA
= k + k
= 2k
Hence ratio between BC and CA is:
Therefore, point C divides BA internally in the ratio 1:2
the point (x, y) is given by
Therefore C(x, y) divides B(–2, –3) and A(4,–1) in the ratio 1:2, then
Point D divides the BD and DA as:
DA = k
BD = BC + CD
= k + k
= 2k
Hence ratio between BD and DA is:
The point D divides the line BA in the ratio 2:1
So now applying section formula again we get,
Question 3.
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs th thedistance AD on the 2nd line and posts a green flag. Preet runs
the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Answer:
It can be observed that Niharika posted the green flag at of the distance AD i.e., 1/4 x 100 = 25 m from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25)
Similarly, Preet posted red flag at of the distance AD i.e., 1/5 x 100 = 20 m from the starting point of 8th line. Therefore, the coordinates of this point R are (8, 20)
According to distance formula, distance between points A(x1, y1) and B(x2, y2) is given by
Distance between these flags by using distance formula, D
= [(8 – 2)2 + (25 – 20)2]1/2
= (36 + 25)1/2
= m
The point at which Rashmi should post her blue flag is the mid-point of the line joining these points. Let this point be A (x,y)
Now by midpoint formula,x = = 5
y = = 22.5
Hence, A (x, y) = (5, 22.5)
Therefore, Rashmi should post her blue flag at 22.5m on 5th line
Question 4.
Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).
Answer:
Let the ratio in which the line segment joining (- 3, 10) and (6, - 8) is divided by point (- 1, 6) be k : 1
Using section formula
i.e. the coordinates of the points P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2,y2), internally in the ratio m : n are
Therefore,
-1 =
⇒ -k – 1 = 6k – 3
⇒ - k -6k = -3 + 1
⇒ 7k = 2
⇒ k =
Therefore, the required ratio is 2: 7.
Question 5.
Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.
Answer:
The diagram for the question is
Let the ratio in which the line segment joining A (1, - 5) and B ( - 4, 5) is divided by x-axis be k: 1
Therefore, the coordinates of the point of division is (,
)
We know that y-coordinate of any point on x-axis is 0
Therefore,
= 0
k = 1
Therefore, x-axis divides it in the ratio 1:1.
Division point = (,
)
= ()
= (, 0)
Question 6.
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Answer:
Let (1, 2), (4, y), (x, 6), and (3, 5) are the coordinates of A, B, C, D vertices of a parallelogram ABCD.
Intersection point O of diagonal AC and BD also divides these diagonals.
Therefore, O is the mid-point of AC and BD.
By mid point formula, If (x, y) is the midpoint of the line joining points A(x1, y1) and B(x2, y2) Then,
If O is the mid-point of AC, then the coordinates of O are:
() = (
, 4)
If O is the mid-point of BD, then the coordinates of O are:
(,
) = (
,
)
Since both the coordinates are of the same point O
Comparing the x coordinates we get,x + 1 = 7
x = 6
And,
Comparing the y coordinates we get, = 4
5 + y = 8
y = 3
Hence, x = 6 and y = 3.
Question 7.
Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4)
Answer:
For points A(x1, y1) and B(x2, y2), the midpoints (x, y) is given by
Let the coordinates of point A be (x, y)
Mid-point of AB is (2, - 3), which is the center of circle and point B is (1, 4)
Therefore,
Therefore, the coordinates
Question 8.
If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such thatand P lies on the line segment AB
Answer:
To find: The coordinates of P
Given: Points A(-2, -2) and B(2, -4) and ratio AP:AB = 3:7
The coordinates of point A and B are ( - 2, - 2) and (2, - 4) respectively
AP = AB
Therefore, AP: PB = 3:4
Point P divides the line segment AB in the ratio 3:4
By section formula,If a point divides the point (x 1, y 1) and (x 2, y 2) in the ratio m:n
then,
(-2/7, -20/7) is the point which divides line in the ratio of 3:4.
Question 9.
Find the coordinates of the points which divide the line segment joining A(– 2, 2) andB (2, 8) into four equal parts
Answer:
It can be observed from the figure that points P, Q, R are dividing the line segment in a ratio 1:3, 1:1, 3:1respectively
Coordinates of X = ()
= (-1, )
Coordinates of Y = ()
= (0, 5)
Coordinates of Z = ()
= (1, )
Question 10.
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken inorder. [Hint: Area of a rhombus (product of its diagonals)]
Answer:
Let (3, 0), (4, 5), ( - 1, 4) and ( - 2, - 1) are the vertices A, B, C, D of a rhombus ABCD
Length of diagonal AC = [(3 + 1)2 + (0 – 4)2]1/2
=
=
Length of diagonal BD = [(4 + 2)2 + (5+ 1)2]1/2
=
= 6
Therefore,
Area of rhombus = 1/2 (Product of the length of the diagonals)Therefore,
Area of rhombus ABCD = 1/2 × × 6
= 1/2 × 48
= 24 square units
Exercise 7.3
Question 1.Find the area of the triangle whose vertices are:
(i) (2, 3), (–1, 0), (2, – 4)
(ii) (–5, –1), (3, –5), (5, 2)
Answer:For a triangle with points A(x1, y1), B(x2, y2) and C(x3, y3)
![](data:image/png;base64,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)
(i) For triangle given: A(2, 3), B(–1, 0), C(2, – 4)
Area of the triangle =
[2 (0+ 4) - 1 (-4 – 3) + 2 (3 – 0)
=
(8 + 7 + 6)
=
Square units
(ii) For triangle given: A(–5, –1), B(3, –5), C(5, 2)
Area of the triangle =
[-5 (-5 – 2) + 3 (2+ 1) + 5 (-1+ 5)
=
(35 + 9 + 20)
= 32 square units
Question 2.In each of the following find the value of ‘k’, for which the points are collinear
(i) (7, –2), (5, 1), (3, k)
(ii) (8, 1), (k, – 4), (2, –5)
Answer:For three points A(x1, y1), B(x2, y2), C(x3, y3)
![](data:image/png;base64,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)
(i)
Collinear points mean that the points lie on a straight line. So,
For collinear points, area of triangle formed by them is zero
Therefore, for points (7, - 2) (5, 1), and (3, k), area = 0
[7 (1 – k) + 5 (k+ 2) + 3 (-2 – 1) = 0
7 – 7 k + 5 k + 10 – 9 = 0
-2 k + 8 = 0
k = 4
(ii) For collinear points, area of triangle formed by them is zero.
Therefore, for points (8, 1), (k, - 4), and (2, - 5), area = 0
[8 (-4+ 5) + k (-5- 1) + 2 (1+ 4) = 0
8 – 6k + 10 = 0
6k = 18
k = 3
Question 3.Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
Answer:Let the vertices of the triangle be A (0, - 1), B (2, 1), C (0, 3)
We know, mid-points of a line joining points (x1, y1) and (x2, y2) is given by
![](data:image/png;base64,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)
Let D, E, F be the mid-points of the sides of this triangle. Coordinates of D, E, and F are given by
![](data:image/png;base64,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)
D = (
,
) = (1, 0)
E = (
) = (0, 1)
F = (
) = (1, 2)
Also, we know area of a triangle having (x1, y1) , (x2, y2) and (x3, y3) is
![](data:image/png;base64,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)
Area of the triangle (DEF) =
[1 (2 – 1) + 1(1- 0) + 0 (0- 2)
=
(1 + 1)
= 1 square unit
Area of the triangle (ABC) = =
[0 (1 – 3) + 2(3 + 1) + 0 (-1 - 1)
=
× 8
= 4 square units
Therefore, required ratio = 1 : 4
Question 4.Find the area of the quadrilateral whose vertices, taken in order, are (– 4, – 2),(–3, – 5), (3, – 2) and (2, 3).
Answer:Let the vertices of the quadrilateral be A ( - 4, - 2), B ( - 3, - 5), C (3, - 2), and D (2, 3). Join AC to form two trianglesΔABC and ΔACD
![](data:image/png;base64,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)
Area of the triangle (ABC) = =
[-4 (-5 + 2) -3 (-2+ 2) + 3 (-2+ 5)]
=
(12 + 0 + 9)
=
Square units
Area of the triangle (ACD) =
[-4 (-2 – 3) + 3(3 + 2) + 2 (-2+ 2)]
=
(20 + 15 + 0)
=
Square units
Area of Quadrilateral ABCD = Area of the triangle (ABC) + Area of the triangle (ACD)
=
+ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 28 Square units
Question 5.You have studied in Class IX, (Chapter 9, Example 3), that a median of a triangle divides it into two triangles of equal areas. Verify this result for Δ ABC whose vertices are A(4, – 6), B(3, –2) and C (5, 2)
Answer:Let the vertices of the triangle be A (4, - 6), B (3, - 2), and C (5, 2)
Let D be the mid-point of side BC of ΔABC Therefore, AD is the median in ΔABC
To prove: Area ΔABC = Area ΔABD + Area ΔADC
![](data:image/png;base64,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)
Midpoint of the line joining the points A(x1, y1) and B(x2, y2) is given by
![](data:image/png;base64,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)
Therefore, by applying the formula we can get the coordinate of D
Coordinates of point D = (
) = (4, 0)
We also know that if A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of a triangle then
Area of triangle is given by,
![](data:image/png;base64,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)
For A (4, - 6), B (3, - 2), and C (5, 2)
Area of the Δ (ABC) = =
[4 (-2 - 2) + 3 (0+ 8) + 5 (-6+ 2)]
=
(-16 + 24 – 20)
= - 6 Square units
However, area cannot be negative. Therefore, area of ΔABC is 6 square units
Now for A(4, -6), D(4, 0), C(5, 2)
Area of the Δ (ADC) = =
[4 (0 - 2) + 4 (2 + 6) + 5 (-6 - 0)]
=
(-8 + 32 – 30)
= - 3 Square units
However, area cannot be negative. Therefore, area of ΔADC is 3 square units
Now for for A(4, -6), B(3, -2) and D(4, 0)
Area of Δ ABD =
[4(-2 - 0) + 3(0 + 6) + 4(-6 +2)]
Area =
[-8 + 18 - 16]
Area = -3 square units
Now the Area cannot be negative so Area of ΔABD = 3 units
Area of Δ ABD + Area of Δ ADC = 3 + 3 square units
Area of Δ ABD + Area of Δ ADC = 6 = Area of Δ ABC
Clearly, median AD has divided ΔABC in two triangles of equal areas
Find the area of the triangle whose vertices are:
(i) (2, 3), (–1, 0), (2, – 4)
(ii) (–5, –1), (3, –5), (5, 2)
Answer:
For a triangle with points A(x1, y1), B(x2, y2) and C(x3, y3)
(i) For triangle given: A(2, 3), B(–1, 0), C(2, – 4)
Area of the triangle = [2 (0+ 4) - 1 (-4 – 3) + 2 (3 – 0)
= (8 + 7 + 6)
= Square units
(ii) For triangle given: A(–5, –1), B(3, –5), C(5, 2)
Area of the triangle = [-5 (-5 – 2) + 3 (2+ 1) + 5 (-1+ 5)
= (35 + 9 + 20)
= 32 square units
Question 2.
In each of the following find the value of ‘k’, for which the points are collinear
(i) (7, –2), (5, 1), (3, k)
(ii) (8, 1), (k, – 4), (2, –5)
Answer:
For three points A(x1, y1), B(x2, y2), C(x3, y3)
(i)
Collinear points mean that the points lie on a straight line. So,
For collinear points, area of triangle formed by them is zero
Therefore, for points (7, - 2) (5, 1), and (3, k), area = 0
[7 (1 – k) + 5 (k+ 2) + 3 (-2 – 1) = 0
7 – 7 k + 5 k + 10 – 9 = 0
-2 k + 8 = 0
k = 4
(ii) For collinear points, area of triangle formed by them is zero.
Therefore, for points (8, 1), (k, - 4), and (2, - 5), area = 0
[8 (-4+ 5) + k (-5- 1) + 2 (1+ 4) = 0
8 – 6k + 10 = 0
6k = 18
k = 3
Question 3.
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
Answer:
Let the vertices of the triangle be A (0, - 1), B (2, 1), C (0, 3)
We know, mid-points of a line joining points (x1, y1) and (x2, y2) is given by
Let D, E, F be the mid-points of the sides of this triangle. Coordinates of D, E, and F are given by
D = (,
) = (1, 0)
E = () = (0, 1)
F = () = (1, 2)
Also, we know area of a triangle having (x1, y1) , (x2, y2) and (x3, y3) is
Area of the triangle (DEF) = [1 (2 – 1) + 1(1- 0) + 0 (0- 2)
= (1 + 1)
= 1 square unit
Area of the triangle (ABC) = = [0 (1 – 3) + 2(3 + 1) + 0 (-1 - 1)
= × 8
= 4 square units
Therefore, required ratio = 1 : 4
Question 4.
Find the area of the quadrilateral whose vertices, taken in order, are (– 4, – 2),(–3, – 5), (3, – 2) and (2, 3).
Answer:
Let the vertices of the quadrilateral be A ( - 4, - 2), B ( - 3, - 5), C (3, - 2), and D (2, 3). Join AC to form two trianglesΔABC and ΔACD
Area of the triangle (ABC) = = [-4 (-5 + 2) -3 (-2+ 2) + 3 (-2+ 5)]
= (12 + 0 + 9)
= Square units
Area of the triangle (ACD) = [-4 (-2 – 3) + 3(3 + 2) + 2 (-2+ 2)]
= (20 + 15 + 0)
= Square units
Area of Quadrilateral ABCD = Area of the triangle (ABC) + Area of the triangle (ACD)
= +
= 28 Square units
Question 5.
You have studied in Class IX, (Chapter 9, Example 3), that a median of a triangle divides it into two triangles of equal areas. Verify this result for Δ ABC whose vertices are A(4, – 6), B(3, –2) and C (5, 2)
Answer:
Let the vertices of the triangle be A (4, - 6), B (3, - 2), and C (5, 2)
Let D be the mid-point of side BC of ΔABC Therefore, AD is the median in ΔABC
To prove: Area ΔABC = Area ΔABD + Area ΔADC
Midpoint of the line joining the points A(x1, y1) and B(x2, y2) is given by
Therefore, by applying the formula we can get the coordinate of D
Coordinates of point D = () = (4, 0)
We also know that if A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of a triangle then
Area of triangle is given by,
For A (4, - 6), B (3, - 2), and C (5, 2)
Area of the Δ (ABC) = = [4 (-2 - 2) + 3 (0+ 8) + 5 (-6+ 2)]
= (-16 + 24 – 20)
= - 6 Square units
However, area cannot be negative. Therefore, area of ΔABC is 6 square units
Now for A(4, -6), D(4, 0), C(5, 2)
Area of the Δ (ADC) = = [4 (0 - 2) + 4 (2 + 6) + 5 (-6 - 0)]
= (-8 + 32 – 30)
= - 3 Square units
However, area cannot be negative. Therefore, area of ΔADC is 3 square units
Now for for A(4, -6), B(3, -2) and D(4, 0)
Area of Δ ABD = [4(-2 - 0) + 3(0 + 6) + 4(-6 +2)]
Area = [-8 + 18 - 16]
Area = -3 square units
Now the Area cannot be negative so Area of ΔABD = 3 units
Area of Δ ABD + Area of Δ ADC = 3 + 3 square units
Area of Δ ABD + Area of Δ ADC = 6 = Area of Δ ABC
Clearly, median AD has divided ΔABC in two triangles of equal areas
Exercise 7.4
Question 1.Determine the ratio in which the line
divides the line segment joining the points A (2, – 2) and B (3, 7)
Answer:Let the given line divide the line segment joining the points A(2, - 2) and B(3, 7) in a ratio k : 1
Coordinates of the point of division = (
)
This point also lies on 2x + y - 4 = 0
Therefore,
2 (
) + (
) – 4 = 0
= 0
9k – 2 = 0
k = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAiCAMAAACk7TNkAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADo6AGa2OgAAOgA6OmZmOma2OpDbZgAAZgA6ZjoAZpDbZrbbZrb/kDoAkLbbkNv/tmYAtv//25A627Zm29u2/7Zm/9uQ/9u2//+2///bgcWJwgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaUlEQVQoU42OSxKAMAhDg3+r1fqtrfX+1xTp6MaFZhMCDDzg1qaJaiC0I2wySdeX0VclZnl8pWiOzRmEhljmOfNVXNusr7X33GtKOuZrevjCwKULMCth3IecsYgqHUFDK9y7xGPI+v/fTjItA+4Stz8gAAAAAElFTkSuQmCC)
Hence, the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A(2, - 2) and B(3, 7) is 2:9.
Question 2.Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear
Answer:If the given points are collinear, then the area of triangle formed by these points will be 0
Area of the triangle =
[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)
=
[x (2 – 0) + 1 (0 – y) + 7 (y – 2)
0 =
(2x – y + 7y – 14)
2x + 6y – 14 = 0
x + 3y – 7 = 0
This is the required relation between x and y
Question 3.Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3)
Answer:The figure for the question is:
![](data:image/png;base64,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)
Let O (x, y) be the centre of the circle. And let the points (6, - 6), (3, - 7), and (3, 3) be representing the points A, B,and C on the circumference of the circle
By distance formula, Distance between two points A(x1, y1) and B(x2, y2) is
AB = √((x2 - x1)2 + (y2 - y1)2)
Then,
OA = √[(x- 6)2 + (y+ 6)2]
OB = √[(x- 3)2 + (y+ 7)2]
OC = √[(x- 3)2 + (y- 3)2]
As OA, OB and OC are radii of same circle, OA = OB
[(x - 6)2 + (y + 6)2]1/2 = [(x - 3)2 + (y + 7)2]1/2
-6x – 2y + 14 = 0
3x + y = 7 (i)
Similarly, OA = OC
[(x - 6)2 + (y + 6)2]1/2 = [(x - 3)2 + (y - 3)2]1/2
-6x + 18y + 54 = 0
-3x + 9y = -27 (ii)
On adding equation (i) and (ii), we obtain
10y = - 20
y = - 2
From equation (i), we obtain
3x - 2 = 7
3x = 9
x = 3
Therefore, the centre of the circle is (3, - 2)
Question 4.The two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of the other two vertices
Answer:Let ABCD be a square having ( - 1, 2) and (3, 2) as vertices A and C respectively. Let (x, y), (x1, y1) be the coordinate of vertex B and D respectively
We know that the sides of a square are equal to each other
![](data:image/png;base64,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)
From the figure we can see that the sides of square AB and BC are equal
And also we know that for two points P(x1, y1) and Q(x2, y2), The distance between points P and Q is given by the formula
PQ = √(x2 - x1)2 + (y2 - y1)2
From the figure,
AB = BC
Therefore,
√[(x + 1)2 + (y - 2)2] = √[(x - 3)2 + (y - 2)2]
Squaring both side, and evaluating
x2 + 2x + 1 + y2 – 4y + 4 = x2 + 9 – 6x + y2 + 4 – 4y
8x = 8
x = 1
We know that in a square, all interior angles are of 90°.
Pythagoras theorem : the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In ΔABC,
Applying pythagoras theorem we get,
AB2 + BC2 = AC2
√[(x + 1)2 + (y - 2)2] 2 + √[(x - 3)2 + (y - 2)2] 2 = √[(3 + 1)2 + (2 - 2)2] 2
4 + y2 + 4 - 4y + 4 + y2 - 4y + 4 =16
2y2 + 16 - 8 y =16
2y2 - 8 y = 0
y(y - 4) = 0
y = 0 or 4
Now we have obtained the B(x, y) point and we are left to find point C(x1, y1)
We know that in a square, the diagonals are equal in length and bisect each other at 90°.
Let O be the mid-point of AC. Therefore, it will also be the mid-point of BD
If O is mid-point of AC, then
we know, mid-point of (x1, y1) and (x2,y2) is
![](data:image/png;base64,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)
i.e.
![](data:image/png;base64,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)
therefore, O = (1, 2)
Also, if we take O as midpoint of BD then
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZoAAAK/CAQAAAD6hsPwAAA7w0lEQVR42u3df3wU1b3/8dfuQkj4kYQgAoVAAgrKb6RiVa60AtqvpaBQERWFYuHS70WFICACXq6iIKW1XNtLi1q1FdGmaGukClZUQMEbv4hK4aZJyw9p0YIVHmi4eTzyeJzvH4zTSbK/dyaZ3X0/95/s7szk7DnnM3POmTMzICIiksk60laZkKAi5Vk2u5w/8zVlQ4L+jb10VzZkpxF8xHhlQ8ICPMAezlVGZJ9SjlKmbEhKDs+yRY20bFNIJU8TUkYknX9/ZJ3yL5sE+S8O0lUZkYJL+IJpyobsMYn/ZYKyIUWrOE5fZUN26MZhNqpp4UITrYrNtFZGZL4A6zlJP2WEC27CcJOyIfNdzBkeVja4og27qaGjMiKzhdjMZ5Rkze/NYx3tPdz+eAx3q1pltkupZ30W/d5O7KWTh9vPoZKjnv4HafH+zLPUMSTN9uZ+DhqYheF2Va3M1Y8v2EGrtKuYfk5bZ47xAXmqXJnqPgzfS8OK6dSDO5lFG/t9N3qmmLbEttjULzBcrcqVmdqyn1MUp3XQlDKLEGtYab0PsYONKaUt0S02NRbDM6pemWkUhq0E41iyA7O4iyuBIOOYw+Sop0LjC5rEthmpT1ZGLlDOq/ZR4SQzU0hb4ltsqpCjHKeLKlgm+gmGO+JYroS5FBLiSeZwG/3owptR14snaBLdZqSG1DSgiKMssT65BsOgFNKW+BbD+S2G76iCZZ5cPsTEMXKWyz3kADCd00wCZmP4fkpBk/g2wyugAJjMF/aMhlVU0c6xRDdW8pDjtZaPWdvgk1UNLiCLvcV4fBfDL1XFMs8A6uOqDuPswFrIxxQB+YxOsXmW+DajNaheZJu1bpDtbGrw7bncHyNo7ucrCW0xHhdQzwFdX5N5ZmJ4Ia4m0JeVuYLXCIRZItG9eTzbjF9nTtjHqC4x+x/xNB0T22L4IZYDSTTqxPfKMcxNYPkO/IWlYb9JZm8ea5vxuwzDRY5xq0EpB01iWwyvApNEsImvteFDDKMTWGMEhlFxLRn/kHP824xsAsYeNl8ds1EUT9oS22J4S9WryTy9qKUuoYmac/nErm5jow5Uxx808W8zWt/sjNVpH8hxyl0I6MS2GN54DO+4PtdCWtQ3MBykQ8zlQpQxGwiylZ1WtS6KMc4Vq2LG3mafBPo5AZbyNKOYwTJqmeFC0ETbYrwpG4Dh75yjipZJ/hXDW3Hs2y/CsJkgw3mFNwgAIebHuGIkVsWMts1chrKOAwnO3SpkGPlMpI4LXWo6Nt1iYik7lxMYhqqiZZK1GH4dx3JFbOMWrmc2HXicmVzNYnqnWDEjb7MbD3IjK6mOO2j6s54+AASpoDzmbiB20ITfYqIpa8M+DN9SRcskL2FYE9eSIS6wJiwG6EnvOJonsStm9G0uSSBoXqCeKwAYw2FKYy6fx49jnJuKtsX4UxZge4Kjk+JzIXYldQY+PqlO2EwkaFZYd9EZxg4Gu5L6aFtMJGXPY/ipqlrmyONPHs6Oir03dy9oCpjHbO5inmtX5kfbYiIpexzD86pqmaMTxzB8w6epS6Rq+jdlSzC8rqqWOYqpx3CJgsbDlM3BUKkzNS1lBA9yL0v5IWvt6R2p6Yvx8dyozAiamRj+h1xV3+Y3gN/zIEXWuwt4lwdduBfmIAwm5tCxgiaVlF2L8e3vyGjf5S+N5madz2csTHm7l2Ac86sUNF4FzTHdzKm53c4/GNnk0/X8I+Xnbl2hoFHQZKJxnGFRmM9vxvDdjA6a5b4NmuUKGj/rxt/4Y9hb7l2L4ekMDZp2LONe3qaKNTzgq9G9xFOmoGl2D2OYHfab72CSuAA3nY40mUFB08y68A9OR7jaZSGGDQ0+CdGLkqivXo1G3IYraJolaI5QoIxoLjdj2BlhaPlFDPMafDKQKmqivqobnZM5O+R8gTLaQzdoyLl5PRZxsl8hRzEMT3H7vWOe3Fzuq5d/UxfZTAwfWDeqkmbwCoZ/DfvNOAyVKRdFNz7H8C8KGg+DpgzDLj2Usfm8huHaMJ+HeAXD5JS3X8hHGL6pjPbQKgyvKBuaz1MYbgjz+RjqqXDhUahnryu8WRntoad1G/Tm70SuaPJpR/7In+ja5PMBfIaJ+jrV6PazQXZiKFNGe2hz3NfGiivy+ROVjiekAOTxaw6GfU59kOIYQ87FTa6dfzatrivsxKMsSKv+wdlrY2eoKjenr3OK+Q267pv5Pd1c2/59GF5Km9y4FYMJMw/Pv9pzUI92an6X8v/4Ty4gj77cy6t8x9U97RQMlS70jiIJMpVHqeAtnnLhRkZ9qeH9CDMkWjpt4XWnFsP5qsbNLchXmcdyZniQ+Rdh+Jt9nY77KV/GtwkAOfyQM65U95KUp6l6l7amRmA4RL4qcSbpxCcYBni09dGO1nwbdnPahf80zqXmmRdpa2oqhjeTvNGu+PYothPDdR5t/XH+wMX2u/kYVqfcsV7p0qXD7qctnB9heFjVLNP8J4YfeLTtCgzr7XfXujAvexZX+TZtTQV4zcNdkrSY8R42IIazznFX5WkYnkppe+2tG/j5MW3hFHKU2jju9ylpppjTnGiG+9oHKPftXtertH1ND9rITCHexHCl5/+nL6eo8OlsX6/SttijnpK0uAXNULQhnmMvXXy62/AmbUFex/A1VbBMdCF17G00WcdtZewJM1vOH7xKW09Os0+Xn2VuA63epXt2RhpseNGzE6j+Tdt0TNQrbSSt3YxhlWdbH8kj9kNe/RY63qUtxDa+sJ7ZKRmokMNUhb1RVOoGs9LuYuc0uqtBS/MybUOo43eaC5DJVmCY6MF2SyhzTAc9j+/56Dd7m7ZHMIxRxcpkPTjOdtfPKHSmkoOOu+Gc8NGzcLxNW1eOsd3D2ePiCw9Qz9dd3uaGRleO1vvo7Li3abuHesaqUmW6czjCVp29dkUXjvI73YEmG0yLcO8bSdQPOOXS43LF53L4PfspVEakaDCndX4me5zHcc2VSlEbXmOnfe5HssAUPm/0zDVJzCKO6+7Y2SXAA/zZt7PE/G8k/2CKsiH7ejbPskXNi6SUcpSFBJQR2acdL7FeJ+YS1pFKfqiB5mxVyJPNcFlaprmDexUyIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIi4ql8bmYqX+dyxjKVb4e5s9YVPMj/5Sbdc0vky6CZxEw+xvAjpnJlk9AYxl4KuJvj9GnmlA1iFUu4h9V6uqT4TxEfs4/cMN8E2MgmQuziAPnNmqbL2UlnALqyi0tVSOIvIzE8HeE4dJi5QC5tmjVF7dnveE7nDXxIOxWT+MliDLdEaCIZRrdAiibyOd3tdyXUMU7FJP4RYCt19A373c3U0qsF0rSBg47HqBdwhMdUUOKnHs0xPmzSowkygsv5FYcZzeWURFm/B3cyy9F860bPFFMUYjf7HFvMo5q3CKqoxE89miebfNqa73ALB3iXqUxlQMS1S5lFiDWstCv8DjY2CoFelER99Wp0c+88qql0PNg2j2r+RJ6KSvzUo7k57DftqOb+GE27MnKBcl61jzMnmdlgmYFUURP1Vc2gBmsU8lGDoGlFJdUKGkmHHs351HNd1LV7MA0o4ihLrE+uwTQKgcR14piCRtKtR3PW/8FwYdS1CygAJvOFfQJyFVUpDw/nc7hJ80xBIz7v0Zy1lENxnNIM8CLbrF5JkO1sSjlNuexnvyOQ86jmw2Y+UySSRI8Gfsfrccw468wJvm/93aVJjya5JuPr1DiezZnPIV7V3DfxU4/mvLDfteFDHoljG5dhuMj6e2yYHs0APsNEfZ1iSKN1VvEp59rvuvE5/6HCEv/0aD6I0PDpzudMjWMbEzAUW3+v5kCTpzcHKY4x5Fzc5BzMUOq42NGEPMNgFZb4w5UYNkT4bpTjCBLNAM5YwwADOU65K+kK8gQ/sRpkAR7lFzq1KX44xjzKy+yjhoO8xIOOsaov3c5HFMbVxFvK04xiBsuoZYZL6cvnGRaQR1sW80s6qMAkHTzDS3F3vgsZRj4TqYsxRJ1Yf2s4C5kf19FOpIUVAK14l1vjWLY/663L04JUUK5mlGSj71HP9ZRSxTlxLP0C9VwBwBgOU6rsk2z0KHvpzd1xnm9ZwQQAhrFDI1ySrXoxlzu4Jc6GVgHzmM1dzKOjsk5ERERERERERERERERERERERERERERERERERERERERERMRPOja5/7REVqTcksv5M19TNsTt39jreFy9ZKERfMR4ZUMCAjzAHseDUCTLlHKUMmVDgnJ4li1qpGWnQip5utHj2CW+nPsj65Rz2SfIf3GQrsqIpFzCF0xTNmSbSfyvdR9qScYqjtNX2ZBNunGYjWpgpNREq2IzrZUR2SLAek5aDz2UZN2E4SZlQ7a4mDM8rGxIURt2U6OnRWSHEJv5jJI0Tf0gVrGEe1jtgyPleAx3q0Jlg0upZ32apv1ydtIZgK7s4tIYS+exjvYepiaHSo7SSVUq8/szz1LHkDiWvJDNcT3fuvm0Zz8T7Xc38CHtoi7fib0eV+lZGG5Xpcp0/fiCHWEeAe90KytYzyGOxVHlvN6bO03kc8e8rxLqGNfCQdOZY3xAnqpVZrsPw/diLDOUEoJsiitovK+Y/7SBg44ALeAIj7V42n6B4WpVq0zWlv2cojiuZf0WNCF2s482jmNcNW9FfTZqPGnrwZ3Mcmy1Gz0TStVYDM+oYmWyURi2xvkQXr8FTR7VVDoalnlU86eoTaPYaStlFiHWsNIOzB1sTChVhRzlOF1UtTLXTzDcEeeybgZNB2ZxF1cCQcYxh8lJzEYo5KMGQdOKSqpTCpoAZeQC5bxqH2dOMjPBdP0Ww3dUtTJVLh9i4ho5czdoSphLISGeZA630Y8uvBl36Dr/0zGXg6YH04AijrLE+uQaDIMSTNd3MfxSlStTDaCeqhjDtO4HTS73kAPAdE4zCZiN4fsJpz6fw02aZw2DphsrecjxWsvHrG3wyaoGV10WUABM5gv7ROmqBPLnSxdQzwFdX5OpZmJ4Ie6l3QqacfaxbSEfUwTkMzqJ5lku+9lPboOg+dDRhYdzuT9G0NzPV5o00V5km5WaINvZlMTgyoEkjk+SJsoxzE0xaBLdm0MPO0AqeI1A0qkP8Do1jj16Pod4Ner24mk6duaEfdTrkkSP5uzvMkmtJ77Xhg8xjE4xaJLZm385GPAXlqb0C1bxqePq/G58zn+k3N+6DMNF1t9jkzxiLFWvJlP1opa6BCZquj3kPALDqJR+wVDquNh+N5IzDE45bRMw9nmr1Un2TcZjeCfGLAtJS9/AcJAOLRY0c/nEXnJsnOeKGgryBD+xGmQBHuUXMbYST9oGcMYaBhjIccqTHGAx/J1zVMUyz79iYpxB9yJoQpQxGwiylZ3Wfy9qMHbWJ4F+Tj7PsIA82rKYX8bcAcQTNAGW8jSjmMEyapnR4Lt4U3YuJzAMVRXLPGsx/DqB5V/i0zjOdMeqmBdh2EyQ4bzCGwSAEPOtS7dyGco6DiQ04THAcBYy3+6HuHEULGQY+UykjgutTxJLWRv2YfiWqljmeQnDmriWvINH2EgVNWxlLQ9H3aPHqphFbOMWrmc2HXicmVzNYnpbHfkHuZGVMU5QpiJ20PRnPX2spl8F5daRMNGUBdie0LikpIkQu5I6pZh6xQxxgTUJMkBPejdq8izxMGjy+HGMU5UvUM8VAIzhMKVJp+x5DD9VJcs0efzJkzlSqU7Y9DJoYlth3cZqGDuajMQlkrLHMTyvSpZpOnEMwzdaYG/u56ApYB6zuYt5YW6QkUjKlmB4XZUs0xRTj+ES36WrZYPGrZTNwTSYFydxGsAPXM22Yla5eCFxX4wvZ0hlRtDMxPA/jnlxEpdL+LXrt6EYwXOubXMQBmONWylo3E7ZtRjf/g7fKmUX3Rp8kui9XIJM5VEqeIunHKfJJrHBmlafelAbx4QRBY37QXNMN3NKRA4vc739LpF7ufwzZJbxbQJADj/kDLPtzze4NP5/hYJGQeMnN7HLcTxI5F4uXxrtmMDRht2cZoD1biCHE7zVg4JGQdOihvBOzHmvOVSGeVZJYkHzOH9wzN+dj2G1fazZzEMZHDTLfRs0yxU0yWlFOQtiLHMZJ8M8ujSxoKnAOG4Vey3GcQXhzVS5MIrmv6BpxzLu5W2qWMMDvhoMTzxlCpoGuvIeI6MusZrtYeYOJxY0w1lnTxaEaRiest/1oS5GCuL7D/480mSGazEcoSCbfnJ3SqK8pnAwyt4myM6ws442Jb3nCVCO4Tr7fR77WdhomRC9oqa5hF6NrsI/O+R8geq3J27ItiHn9uzDxHidZHqEK1HyOcydrgZNX05R4RhYCPAGzzZaZiBV1ER9VTc6kdnbpyc3M8NMDB+4dHIgY5TyOlsYHuabYuq5wcWgCfEcextdx7LJuhIlFd34HMO/RFnC+OTl13SZKHlXhmGXHsfYtDJPZR+7WNToicgDMVzrYtCUsafJM5d/48K8pkI+wvBNFaQnVmF4RdnQNGgmspdd3O1p0IznRYrCbCv1oDl7deHNKkhPPK3boIdrhL3MFkZ43DwbySP2WSFn6DzvQvMsyE4MZSpKT2yO+6rYDJHP2zE61TX8lZkRBgIKOBJ2okviQTOYlXZXMod5joGA7U0GAgbwWYz296km92x+VlcXetYK2YVpdFOOjBd9yHk8h7g86h785zGCphOPsiBGN7GEMsdT6c9zPHipLf/T5ARrkOIYQ87FTYL8PgwvpUFpxJNb/tKeg3q0k1NXPmBM1CVW83aYInbey+VWDCbqCcrOVHLQcWQ74bjG8jzqwjYMEzUFQ6UjMP0qdm75b6dbi+F8BcuXB95n7McwRHIppxucaW96L5e+1PC+PXM5nA2NGlf1jps83Mx+V+5JfxGGv4UZZnBD+AsbkhM7t1oqZZGMwHCIfIXLWUN4N+a8rxwqYz7FEkr4bpKFvpllLjV7PsHYs6fdDZnwFzYkL9nc8j5l4UzF8GZS9wzNYpOpbPDIh3DGJdng6M/BRpe3JV+BdjaYnuOeyBc2JGucS80z91MWzo8wPKwwSEwOFdwSo5m3MqkryINscPFeZf+J4Qce/P7IFzYk2yhe6dL19m6nLJwAr3m0M8pwpVQ2utVcQ7O4KqntTnTtcmesu9t70YyIdmFDMpLNLe9TFk4hR6mNWvoSwXDKI94ToL11S7rEt/mcqzfrKOY0Jzy4u320CxsSl2xueZ+y8L6mB20krx+rXL6F04MJPBgjvmbPmxiu9DQXGl/Y4B9epWyxJ40+8Y0Fnhdw4wsb/MOblAV5HcPXVLUy14XUsTfmSF8qx7KmFzb4g1cp68lp9umOZ5ksxJvUx/Vsl+SEu7DBH7xK2XQMy1WxMtvNGFZ5tO3wFzb4gVcpC7GNL6zHD0rGKuSwK3e3aSrShQ0tz7uUDaGO32kuQOZbgWGi61uNdGFDy/MyZY9gYkznlYzQg+Nsd/m8QuQLG1qalynryjG2p8G8cXHBA9TzdRe3F+3ChpblbcruoZ6xqk7Z4RyOsNXFY020Cxtalpcp68JRfqc70GSPaRFuByLx+wGnmjynUzJYDr9nv+sPocomgzmt8zPZ5jyOa8ZU0trwGjtduZ5W0soUPmeUsiEpiziu+2JnowAP8GefTnrxt5H8gynKhmzt2TzLFjUyElTKURamfPNGSVvteIn1Oj2XgI5U8kMNNGe3Qp70+LK0zHIH9ypkRERERERERERERERERERERERERERERERERERERERERERERLLaIFaxhHtYrQcGisTjcnbSGYCu7OLSGEvnsc6ThzRmpAvZrLvxZ6D27Hc8dPEGPqRd1OU7sZdOyrZYbmUF6znEsTgyS/uhdDORz+luvyuhjnEKmtQNpYQgm+IKGmVputnAQcduroAjPKYSdouCJhOF2M0+2jhaCtW8FfVR6PGUcA/uZJZjq93oqaBR0GSKPKqpdDylNI9q/kReSiVcyixCrGGlHZg72KigSTVoOjCLu7gSCDKOOUzWrbdbSCEfNQiaVlRSnVLQBCgjFyjnVfs4c5KZCprUgqaEuRQS4knmcBv96MKb3KH62yI6cczloOnBNKCIoyyxPrkGwyAFTSpBk8s95AAwndNMAmZj+L7qb4vI53CT5lnDoOnGSh5yvNbyMWsbfLLKMfoGBRQAk/nCPlG6iqoYw9gKmhhLjWOI9ddCPqYIyGe0mmctJJf97Ce3QdB86OjCw7ncHyNo7ucrTZpoL7LNKtMg29mUrdkbPmgS3Q9BDztAKnhND6trYQFep8bxoMV8DvFq1FKJpwHemRN226FL9vZoIgVNMvuhLwcD/sJS1doWt4pPOdexE/yc/0i513oZhousv8dmb4/G/SHnERg9uNwHhlLHxfa7kZxhcMolPAFDsfX3ag5k7yOD3Q6auXxiLzk26uk08VKQJ/iJ1SAL8Ci/iFEW8ZTwAM5YwwADOU559mauO0EToozZQJCt7LSKp6jB2Fkf9XOaWT7PsIA82rKYX9LBhd1igKU8zShmsIxaZjT4LqvK9yU+pUvKQXMRhs0EGc4rvEEACDGfjtZIzlDWcSDqWQLxZjhgOAuZb/dD3GhLFDKMfCZSx4XWJ1lVvnfwCBupooatrOXhqPuiWFlaxDZu4Xpm04HHmcnVLKa31QV9kBtZGePUmrS02EHTn/X0sZp+FZRb7QmVbwpZGuICa/pegJ70bnSwXqJM9bk8fhzjVOUL1HMFAGM4TKnK172BgPCUqelvBRMAGMaOJiNxKt+k9kMKmkxXwDxmcxfzrL6qytdjylSVryhTReWrTPVaR2ZyHw/RV+UrLZmp6XQvnY5MYRO19FL5xiHIVB6lgrd4iqEKGnckci8d/1jHu46rXFS+kUNmGd8mAOTwQ84wW0HjhkTupeMXrdnDT1W+cRjtmKTTht2cZoB3iR/CO76ce7rco+ZZegVNb2q5LiODxu3yfZw/OOZoz8ew2rvEt6KcBb7KznYs417epoo1PMAlWR0012dgj8ab8q3AsN5+dy3G26tEu/IeI7Om2de8QRNiAvOZTg6t7OtUA1zPQmvC/DDKWMzYRlOI/rnWzzK0R+O+4ayzJ4TCNAxPpbrJ7pREeU3hoOt7dK8rY6+ov6iEXhHuNtCcQdOb15hCkK+wgO0stz4dz1c5n8OUMocrCJDLm8yJsNbeDO3ReFe+Z3dL5ZhUm7Xt2YeJ8TrJ9DS6AGwgVdREfVVHuLS2+YKmlENMcez5brSqw1wCdKeW5+17Jqxw3Muy8VrXZWXQJF++AH05RYV1pyOPi/h1tjA8bJfNH6/0ap61poKddtNqErXWhQ+lTAHGYPiWvewzdtA0XcvrHs3yDCtfCPEce+O44sulfzaVfexiEV0VNCm7CuMYBP0Z71l7vrN3A1tBjX01Ug7vsS7CWntoraBJUBl7GtVgT4NmInvZxd3N9y8zeCDgOers6S/OsMC6A9gL9rv+1DE+jrUkHuN5kaLm+mfFvMwWRmj0zBVt2McH9q32elPLZMe3XTjpOGO9gL9zToS1JikKEjKSR+yzjimGTj5vx+hW1fBXZqbRQMAAPosxsHHKvn9nSwRNHtWOY8kUq0cz0srhsRg7da35b34FhBgVZq1Sx1rZJLnyHcxKu/ufw7xUExF9yHk8h7g8rTI1SHGMIcniCFWteYKmNXt43B4A3cD75BDiduuTVVTbj08aRj3fBPoxvslae2jtWCubJFO+JZQ5eoDn8T0vE9iVDxiTNcUR3710UreYLVax3sg7/AHobz2OL8h2fmsvdw3H6ESA22nXZK1XHWtJdJ2p5KCj5XSCb3jZ/X/GfhSCF3sM/0zXTuReOqlry88pYzSLGM5AdnMV/27dXryAI44RsiJ2M4k51jX0kdfy6xHBL+W7oVHzrb7RjTxcNYR3PXugbLZP1+5Bf+u8dVsGOpoOPRuczW7DoAZTZiOt5ceQ0XR81zXrdG1R+WaCZp2uLSrfTNDM07VF5Zv+PJiuLSrf7OHKdG1R+WaTZpuuLSrfzNCs07VF5ZsJmnW6tqh801+zTtcWlW/6c3G6tqh8s4HL07VF5ZvpmnW6tqh801+zTtcWlW8maNbp2qLyFRERERERERERERERERERERERERERERERERERERERERER73RkJvfxEH0z7pd1VuH614VspjCNg2YKm6ilV4aVynDeoJUqp//cygrWc4hjdErr37GOdzOsgrXlLSoVNH40lBKCbErzoGnNHn6aYSVzG0cUNP80hHcaPJC75aV70PSmNsOeCDaY69imoPmnVpSzQEHjouszrEeTyyJCCpqGuvIeI2Mu1YFZ3MWVQJBxzGEyoQwNmhATmM90cmhl/8YA17OQfgAMo4zFjCUQYa2fNUuPpgd3Mos29vtu9PSsp1kC2Rg03SmJ8prCQS6Jun4JcykkxJPM4Tb60YU3uSNG1esV9X+W0CtC2LVs0PTmNaYQ5CssYDvLrU/H81XO5zClzOEKAuTyJnMirLW3GXo0pcwixBpW2rm9g42elEc/boJsDJr27Gt0q+qmr5NMJxjxAH2P9QyS6ZxmEjAbw/ej/s+BVDnuJx/uVc0g3wVNKYeYYv09DcONVoWbS4Du1PI83a1vV/CWnV+N1/K6RxOgjFygnFft48xJZnpQHjkssB6loeZZ2OryOlsYHva7cQyx/lrIxxQB+YzOwOZZayrYaVeNSdTS28qbKcAYDN+yl33GDpqma3ndo+nBNKCIoyyxPrkGE2EXlJob7ZO0CpoIB/Cp7GMXi5o8crSHHSAVvNaoLZ9JQXMVhhn2u5/xnnV8LaAAWEENHew98Husi7DWHsdjjrxxNj2T+cLqZcEqqmjn+v/pwy323wqaCEEzkb3s4u6Iz+ntwF9YmsGjZ89RZ+9ZnWEBEGQ7L9jv+lPH+DjW8rKJ9iLbrJ1ZkO1scv0/tGKRY6BBQRNGMS+zhRFRlxmBYVTGBk0b9vGBXU16U8tkx7ddOMls+90C/s45Edaa1Cyp7cwJu1fZJWaPJhmXsY0n7NffOM5TPMGF2RIQ+bwdoxNYw1+ZGXEg4Etz+cSuzmNjLD2Az2IMPZyye0r+CJo8qh3HkilWj2ak9TvHYuz0tua/+RUQYlSYtUoda3nnMgwX2WURu0eTfHmcPepUasi54Ws8h7g8SrOtjNlAkK3stCpDUYOxsz5h+jlBimMMcRZHqFgtFTSt2cPjduNnA++TQ4jb7V5DNe2tv4dRzzeBfoxvstYeWjvW8s4EDMXW36s5EHNWR/LlkbVBE01XPmBMlO8vwrCZIMN5hTcIACHm0xGAXIayjgPkuZiel/iULi2SE4vZYlWcG3mHPwD9GWf3Gn5rL3cNx+hEgNtp12StVx1reWkAZ6xhgIEcp9zzo/B+3rcffa7uP8/YA5fhFbGNW7ie2XTgcWZyNYutodhuPMiNrKTapaC5g0fYSBU1bGUtD9tjVc2lLT+njNEsYjgD2c1V/Du51njVEccIWRG7mcQcBsdYy9uBgKU8zShmsIxaR9oiHfmT15PH+A011PAsj3k27yCtDOFdu9kRObAusDIrQE96NyqSJa4FjR/0oL81JtWWgY7B454Nzku1YVCDBlGktbxVyDDymUid3T334sgvHsisoEkP/VlPH6vhWEG51Tx0+8gvCpoM8gL1XAHAGA5TqvJQ0EgsK5gAwDB2WD0rlYeCRqIqYB6zuYt51iimykNBIyoPFZKoPESFpPIQFZLKQ5rNchWSgkbi1Y5l3MvbVLGGB2LcZUAUNCI68ovoyC8iIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiWSqfm5nK17mcsUzl2wSaLHEFD/J/uSnMN97rrAISPwbNJGbyMYYfMZUrm4TGMPZSwN0cp0+zp204b9BKRSR+VMTH7CM3zDcBNrKJELs4QH4zp6otb1GpoBF/Gonh6QjHocPMBXJp0+ypuo0jChrxq8UYbgn7zSAMo1skTYO5jm0KGvGnAFupo2/Y726mll4tkKZcFhFS0Ih/ezTH+LBJjybICC7nVxxmNJdTEnbNHtzJLEfDrRs9XUrTrZSAgkb83KN5ssmnrfkOt3CAd5nKVAaEWa+UWYRYw0rrfYgdbGywRIhelER99SIUZsv9uAkUNOLvHs3NYb9pRzX3R2zUlZELlPOqfZw5ycwGywykipqor2oGNdlyDgtoraCR9OzRnE8910VYrwfTgCKOssT65BpMmBBI3I12ahQ0kkY9mrP+D4YLI6xXQAEwmS/oZ32yiirapZyePo5xPAWNpFGP5qylHIp6SjPAi2yzeiVBtrMp5dS0YpFjYEFBI2nWo4Hf8XrUGWedOcH3rb+7NOnRJOMytvGE/fobx3mKJyIe7URarEdzXtjv2vAhj8So4oaLrL/HhunRDOAzTNTXKYZEOepU6kgj/uzRfBBhikx3Pmdq1LUnYCi2/l7NAdo2+j5IcYwh52KCChpJL1di2BDhu1GO40h4AzhjDQMM5DjlLqctj/28T44KSfxzjHmUl9lHDQd5iQfD7NFv5yMKYzTulvI0o5jBMmqZ4WLqevIYv6GGGp7lMdfmGYh47BleiuPCs0KGkc9E6tRdl2xWALTiXW6NulR/1lsXpgWpoDxK70Qkw32Peq6nlCrOibrcC9RzBQBjOEypMk6y16PspTd3xzzrsoIJAAxjB4OVbZLNejGXO7glZnOrgHnM5i7m0VGZJiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIu7o2OSZOhJZkXJLLufPfE3ZELd/Yy/dlQ3ZbAQfMV7ZkIAAD7CHc5UR2aqUo5QpGxKUw7NsUSMtOxVSydPWw9wlsZz7I+uUc9knyH9xkK7KiKRcwhdMUzZkm0n8r/VsHUnGKo7TV9mQTbpxmI1qYKTURKtiM62VEdkiwHpOWg9yl2TdhOEmZUO2uJgzPJz2v6JzC///NuymRk/Ayw4hNvMZJWn+K4bzBq1aOA3jMdytCpUNLqWe9Wn+G9ryFpUxgyaPdbT3MBU5VHKUTqpSmd+feZY6hsSx5IVsptCnv+I2jsQRNJ3Y63GVnoXhdlWqTNePL9gRo7rdygrWc4hjcVQ5r/fm4QzmOrb5Img6c4wPyFO1ymz3YfhejGWGUkKQTXEFjfcVs7FcFhHySdDALzBcrWqVydqyn1MUx7WsX4PmVkrAtaDpwZ3Moo39vhs9E0rNWAzPqGJlslEYthJM46DpZ50bcSdoSplFiDWstN6H2MHGhNJTyFGO00VVK3P9BMMdcS7rZtB0YBZ3cSUQZBxzmJzkbIQcFlhn4d0ImgBl5ALlvGofZ04yM8E0/RbDd1S1MlUuH2LiGjlzN2hKmEshIZ5kDrfRjy68GXfoNnSjPd/LjaDpwTSgiKMssT65BsOgBNP0XQy/VOXKVAOop4p2zRw0udxDDgDTOc0kYDaG7yeR/j7cYv8dLmi6sZKHHK+1fMzaBp+sanDVZQEFwGS+sKcUrUogf750AfUc0PU1mWomhhfiXtqtoBlnH9sW8jFFQD6jk2ietWKRo8MeLmjO5f4YQXM/X2nSRHuRbVZqgmxnUxKDKweSOD5JmijHMDfFoEl0bw497ACp4DUCSaf+MrbxhP36G8d5iie4MMWmY2dO2Ee9Lkn0aM7+LpPUeuJ7bfgQw+gUgyaZvfmXgwF/YalLv6UVlS4NOV+G4SLr77FJHjGWqleTqXpRS10CEzXdHnIegWGU74JmAsY+b7U6yb7JeAzvtPj0UfHANzAcpEOLBc1cPrGXHBvnuaJI8tjP+9bwQmppG8AZaxhgIMcpT3KAxfB3zlEVyzz/iuGtBCqrO0EToozZQJCt7LT+e1GDsbM+CfZzevIYv6GGGp7lsajn7+MJmgBLeZpRzGAZtcxo8F28KTuXExiGqoplnrUYfp3A8i/xaRxnumNVzIswbCbIcF7hDQJAiPnWpVu5DGUdBzyb8BjvUbCQYeQzkTp7WCGxlLVhH4ZvqYplnpcwrIlryTt4hI1UUcNW1vJw1CZdrIpZxDZu4Xpm04HHmcnVLKY3AN14kBtZSXULBk1/1tMHgCAVlFtHwkRTFmB7QuOSkiZC7ErylGKqFTPEBVYjKkBPejdq8izxMGjy+HGMU5UvUM8VAIzhMKVJp+x5DD9VJcs0efzJkzlSqU7Y9DJoYlth3cZqGDsYnELKHsfwvCpZpunEMQzfaIG9uZ+DpoB5zOYu5oW5QUYiKVuC4XVVskxTTD2GS3yXrpYNGrdSNgcTx3kjiWAAP3Ap84pZ5eKFxH0xvpwhlRlBMxPD/5Cr6p+MS/i1izejGMFzrm1tEAZjjVspaNxO2bUY3/4OnytlF90afBL/HV2CTOVRKniLpxynySaxIeZ573jD2TgmjCho3A+aY7qZU+JyeJnr7XeJ3NEFgizj2wSAHH7IGWbbn29wafz/CgWNgsZ/bmKX46iQyB1dYLRjAkcbdnOaAda7gRxO8FYPChoFjQ8M4Z2Ys19zqAzzxJJ4g+Zx/sDF9rv5GFbbx5rNPJTBQbPct0GzXEGTilaUsyDGMpdxMswDTOMNmgqM41ax12IcVxDeTJULo2j+C5p2LONe3qaKNTzgq8HwxFOmoAmjK+8xMuoSq9keZgZxvEEznHWOaxCnYXjKfteHuhj/m7j+gz+PNJnhWgxHKMi+H96dkiivKRyMss8JsjPs3KNNSex/ApRjuM5+n8d+FjZaJkSvqKktoVejq/DPDjlfoPrtiRuyc8i5PfswMV4nmR7hepR8DnOnS0HTl1NUOIYUArzBs42WGUgVNVFf1Y1OZPb26cnNzDATwwcunRzIMKW8zhaGh/mmmHpucCVoQjzH3kbXsWyyrkRJRTc+x/AvUZYwPnn5NV0mSt6VYdilxzFGqtJT2ccuFjV6LvJADNe6EjRl7GnyzOXfuDCvqZCPMHxTReiJVRheUTZECpqJ7GUXd3sUNON5kaIwW0k9aM5eXXizitATT+s26JEU8zJbGOFZ82wkj9jng5yh87wLzbMgOzGUqRA9sTnuq2IzSj5vx+ha1/BXZkYYCCjgSNjpLokEzWBW2l3JHOY5BgK2NxkIGMBnMdrfp5rcs/lZXV3oWftjF6bRTTmyRPQh5/Ec4vKo+/GfxwiaTjzKgoidxRLKHE+lP8/x4KW2/E+TU6tBimMMORc3Ce/7MLyUBuUQPZ/8qD0H9WinprryAWOiLrGat8MUtPOOLrdiMBFOU3amkoOOY9oJxzWW51EXtkmYqCkYKh2B6VfR8smvu9taDOcrTBoefp+xH8YQyaWcbnC+vekdXfpSw/v2/OWGNjRqXNU7bvJwM/tduSf9RRj+FmaYwQ3hL2xITrR8atmURTICwyHyFShOQ3g35uyvHCpjPssSSvhuwoW+mWUuNXs+wdizp90NmfAXNiQv8XxqrpSFMxXDmyneMzRLTabS8SiI8MYl3Ozoz8FGF7YlX4F2Npie457IFzYka5xLzTP3UxbOjzA8rABIRg4VjocOhW/mrUzwOvIgG1y8V9l/YviBB7888oUNyTaHV7p0vb3bKQsnwGse7YyyQimVjW4419AsrkpwixNdu9wZ6+72XjQjol3YkIzE86m5UhZOIUepjVruEtVwyiPeE6C9dWO6RLb2nIu36YBiTnPCg7vbR7uwIXGJ51NzpSy8r+lBG6nqxyrXbuH0YAIPxoiv2fMmhis9/f2NL2zwD69SttiTRp/4xgLPC7jxhQ3+4U3KgryO4WuqWpnrQurYG3OML5VjWdMLG/zBq5T15DT7dMezTBbiTertZ0y6L9yFDf7gVcqmY1iuipXZbsawyqNth7+wwQ+8SlmIbXxhPX5QMlYhh125u01TkS5saHnepWwIdfxOcwEy3woME13faqQLG1qelyl7BBNjIq9khB4cZ7vL5xUiX9jQ0rxMWVeOsT0N5o2LCx6gnq+7uL1oFza0LG9Tdg/1jFV1yg7ncIStLh5rol3Y0LK8TFkXjvI73YEme0yLcCMQid8PONXkOZ2SwXL4PftdndeWbQZzWudnss15HNeMqaS14TV2unI9raSVKXzOKGVDUhZxXPfFzkYBHuDPPp304m8j+QdTlA3Z2rN5li1qZCSolKMsTPnmjZK22vES63V6LgEdqeSHGmjOboU86fFlaZnlDu5VyIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiP91VhaIJGI4b7j8pB6RjNaWt6iMGTR5rPPkcYvSyIVs1j35fe82jsQRNJ3YSydllpduZQXrOcSxODJa+7CWNJjr2Kag8YOhlBBkU1xBo+JoObksIqSg8RMFjf9bBCXgWtD04E5m0cZ+342eymIFTWbpx03gWtCUMosQa1hpvQ+xg43K5JYMmg7M4i6uBIKMYw6TdQPuFOWwwHpSghtBE6CMXKCcV+3jzElmKptbLmhKmEshIZ5kDrfRjy68yR3K4JTcSF/rLzeCpgfTgCKOssT65BoMg5TNLRU0udxDDgDTOc0kYDaG7yuDU9CHW+y/wwVNN1bykOO1lo9Z2+CTVXR3LF9AATCZL+hnfbKKKtopo1sqaMYxxPprIR9TBOQzWs2zFLRikaPDHi5ozuX+GEFzP19p0kR7kW1WuQTZziZltFtBk+g+DHrYAVLBa3pknQsuYxtP2K+/cZyneIILU2xEd+aEffzvoh6Nm0GTzD7sy8GAv7BU2er6UafSpSHnyzBcZP09Vj2alh4IOGsERo8v93HQTMBQbP29mgN6+K8fgmYun9hLjiWoDHZFHvt53xpoSa2UBnDGGgYYyHHKlbUtFzQhypgNBNnKTitUihqMnfVRPydJPXmM31BDDc/yWNTz9/EETYClPM0oZrCMWmY0+E5lFKeX+JQuKQfNRRg2E2Q4r/AGASDEfDoCkMtQ1nGAPGW2x+JtDxQyjHwmUmcPK6iM4nQHj7CRKmrYyloepkMKxVHENm7hembTgceZydUspjcA3XiQG1lJtQrEB0HTn/X0ASBIBeVWm0Bl1ELFEeICq+kQoCe9Gx3ol6hAmqXn8+MYpypfoJ4rABjDYUpVRn448EeiAvGHFUwAYBg7GKwyaul9mIImHRQwj9ncxTyrv6ky8jEViMpIVCAqI1GBpK4jM7mPh+zp/Coj8WGB+OteOh2ZwiZq6aUyAiDIVB6lgrd4iqEKgpYvkETupdOc1vFumt7Uz+0yCrKMbxMAcvghZ5itMGjpoEnkXjrNpzV7+KnKCIDRjkk6bdjNaQb484cP4R1fzltd7lHzzG9B05tarkvToHG7jB7nD1xsv5uPYbU/f3grylngqxS1Yxn38jZVrOEBLsnwoLk+LXs03pRRBYb19rtrMf69SrQr7zEya5p9bgdNiAnMZzo5tLKvRA1wPQut6fTDKGMxYxtNEvrnWj9L2x6N+4azznGd6TQMT7VkcrpTEuU1hYOu79G9FaJX1F9UQq8IdxtwN2h68xpTCPIVFrCd5dan4/kq53OYUuZwBQFyeZM5Edbam7Y9Gu/K6OyOpxzTkg3X9uzDxHidZHoaXQA2kCpqor6qI1yW62bQlHKIKY794o1WZZlLgO7U8rx9V4QVvGXnbuO1rsvQoEm+jAD6coqKmBfRtbBSXmcLw8N29/zx8lvzrDUV7LSbVpOotS5tKGUKMAbDt+xln7GDpulaqfdolmdYGUGI59gbx1VbPjicTmUfu1hEVwVNHK7COIZIf8Z71n7x7L3CVlBjX2+Uw3usi7DWHut+mAoapzL2NKqFvg2aiexlF3enR3JbPGieo86e/uIMC6z7g71gv+tPHePjWEu+7BO+SFE6JLSYl9nCCI2exakN+/jAvjVfb2qZ7Pi2Cycd57MX8HfOibDWJMVIIyN5xD5z2IKhk8/bMbpkNfyVmWk0EDCAz2IMbJyy79/pTdDkUe04lkyxejQjrTwci7H/f2v+m18BIUaFWavUsVZmSa6MBrPS7v7nMK8lf0D0IefxHOLytCqQIMUxhjOLI1REt4KmNXt43B4e3cD75BDiduuTVVTbz4EbRj3fBPoxvslae2jtWCuzJFNGJZQ5+njn8T2//riufMCYrDn4x3cvnXgsZotV6DfyDn8A+jPO7tH81l7uGo7RiQC3067JWq861pLOVHLQ0fo5wTf82v1/xn6Mghd7G/9M9U7kXjrxaMvPKWM0ixjOQHZzFf9OrjV+dsQxQlbEbiYxx7rCPvJaLXdE8EsZbWjUfKtvdCMP3xjCu549UDbzp3r3oL91VrstAx0Ni54NznW3YVCDSbGR1mqZkNF0fF9Jm6neKiOVkV+kzVRvlZHKyC/SaKq3ykhl5A8+m+otKqP00uJTvUVllG7SYqq3ykhl5B9pM9VbZaSM8Iu0meqtMhJ/SJup3ioj8QefTPUWlVG68NFUb1EZpYO0meqtMlIZ+UPaTPVWGamM/CJtpnqrjFRGIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiKSnjoyk/t4iL7KCvGXC9lMoU+DZgqbqKVX2uTlIFaxhHtYTT9VrMx0KytYzyGO0cm3aVzHu7RKk/y8nJ10BqAru7hUFSwTDaWEIJt8HDSt2cNP0yQ327Ofifa7G/iQdqpi7hjCO/bjfPzBz0HTm9q0efrxRD6nu/2uhDrGqbq7oxXlLFDQxOn6NOrRbOAg7e13BRzhMVV3t3TlPUbGXKoDs7iLK4Eg45jDZEJpGDQhJjCf6eTQyk5/gOtZaHWUh1HGYsYSiLDWz1zq0fTgTmbRxn7fjZ6u/9Ld7HP8hzyqeYugqnv8ulMS5TWFg1wSdf0S5lJIiCeZw230owtvckeMQusV9X+W0CtC2HkXNL15jSkE+QoL2M5y69PxfJXzOUwpc7iCALm8yZwIa+11pUdTyixCrGGlnVc72OhybuZRTaUjwPOo5k/kKRTi7xLua/Tonqavk0yPuB/K5R7rmYzTOc0kYDaG70f9nwOpcjxfK9yrmkHNGjSlHGKK9fc0DDda1XEuAbpTy/N2D2CFY5/ceK3UezQBysgFynnVPs6cZKbLuVnIRw2CphWVVCto3K5Sr7OF4WG/G8cQ66+FfEwRkM/oNGuetaaCnXYlmkQtva3fPQUYg+Fb9rLP2EHTdK3UezQ9mAYUcZQl1ifXYCLsQJLXiWMKGu+FmMo+drGIrk2K+csAqeC1Ru39dAmaqzDMsN/9jPesY2cBBcAKauhgfZfDe6yLsNYexyNdk3X2P07mC/uE4yqqXB8Ozudwk+aZgsaDoJnIXnZxd5Og+edgwF9YmqajZ89RZ09/cYYFQJDtvGC/608d4+NYK7Um2otss3ZFQbazyfXfm8t+9pPbIGg+dAwMiAuKeZktjIi6zAgMo9IyaNqwjw/sKtObWiY7vu3CSWbb7xbwd86JsNYkl9LTmRN2n7BLzB5NcmH5OjWOM3D5HOJVz1sJGSSft2N0I2v4KzNjDkjO5RO7Oo+NsfQAPosx9HDK7il5HzR5VDuOJVOsHs1I6zeMxdhpac1/8ysgxKgwa5U61krFZRgusnMydo8mmdxcxaeca7/rxuf8h0IhEdGHnMdziMujNNvKmA0E2cpOq8IUNRg76xNmDxakOMYgaXGEyudF0LRmD4/b++ANvE8OIW63q1e1fRpwGPV8E+jH+CZr7aG1Y61UTMBQbP29mgMx52Qkk5tDqeNi+91IzjBYgeCWrnzAmCjfX4RhM0GG8wpvEABCzKej1XIeyjoOuNrBfIlP6eL6r1zMFqta3cg7/AHob00rCbKd39rLXcMxOhHgdto1WetVx1qpGcAZaxhgIMcp96RcgzzBT6zdWYBH+YVObbrX/X/GHvoMr4ht3ML1zKYDjzOTq1lsDdd240FuZKVrozJ38AgbqaKGrazlYXs8yw1t+TlljGYRwxnIbq7i361ucgFHHCNkRexmEnOsvXLktVLtcSzlaUYxg2XUOv57pON2ss3yZ1hAHm1ZzC9dzc0sN4R3HTOUIgXWBdY0jwA96d2oUJekzVBmD/pbI1ZtGegYPO7Z4JxTGwY1aC5FWitVhQwjn4nUcaE94uX2cTvAcBYy3+4/iU8s0fh/gvqznj5WE6qCcqvZ5PZxWxQ0GeQF6rkCgDEcplS5qaCRWFYwAYBh7GgyoqXcVNBIGAXMYzZ3Mc8ag1RuKmhEuSkqZuWmqJiVm6JiVm5KGlmuYlbQSLzasYx7eZsq1vBAjLsMiIJGRMdtER23RURERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERES88v8B4hSfjWCTqEMAAAAASUVORK5CYII=)
Therefore, The sides of square are A(-1, 2), B(1, 4), C(1, 0) and D(3, 2)
or A(-1, 2), B(1, 0), C(1, 4) and D(3, 2)
Question 5.The Class X students of asecondary school inKrishinagarhave been allotteda rectangular plot of land fortheir gardening activity.Sapling of Gulmohar areplanted on the boundary at adistance of 1m from each other.There is a triangular grassylawn in the plot as shown inthe Fig. 7.14. The students areto sow seeds of floweringplants on the remaining area of the plot
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?
![](data:image/png;base64,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)
Answer:(i) Taking A as origin,
We will take AD as x-axis and AB as y-axis.
It can be observed that the coordinates of point P,Q, and R are (4, 6), (3, 2), and (6, 5) respectively
Area of the triangle PQR =
[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)
=
[4 (2 – 5) + 3 (5 – 6) + 6 (6 – 2)
=
(-12 – 3 + 24)
=
Square units
(ii) Taking C as origin, CB as x-axis, and CD as y-axis, the coordinates of vertices P, Q, and R are (12, 2), (13, 6),and (10, 3) respectively
Area of the triangle PQR =
[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 - y2)
=
[12 (6 – 3) + 13 (3 – 2) + 10 (2 – 6)
=
(36 + 13 – 40)
=
Square units
It can be observed that the area of the triangle is same in both the cases
Question 6.The vertices of a Δ ABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that
Calculate the area of theΔ ADE and compare it with the area of Δ ABC (Recall Theorem 6.2 and Theorem 6.6)
Answer:Given that,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANsAAADSCAAAAADm5+pUAAAABGdBTUEAALGOfPtRkwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABpISURBVHja7Z1plNXFlcD5NB/mw3ydM3NOMnGWTI4xEYyCCCIB1AiKUYPIIgKyaBIhiqJGMYKaoEYFBSOEKCoSRUURBWUxAo1ssiooSzfQ+/KW/1Z71b1z6yHENLS8brr7vceZ6rZPo037//3rrlW3bnXBThkguJNCWg3YeaNLJ7ElqFFJy89CNnQ8ERihPRvZIKPjpD5CPPvYQAnQGRGelfpmIKOkgbNS3xAiLp7MurNQJv3Q+77zEReIhpPZPGn+4BtfS4zNpEA/2//OSHJmkizI5v/dERWAcyXJlkU1bdYFR1AKVLUsbj5r1uukNiXJhiJe8cXRrq/HBGclr4NTsClhSlPfZDJk8eIf/EZgYwLayVOoG2jlSpENIvnxGx999FjXz5GDa4pP9TPOtrMV7Sw2Fo9ViOx7dzWhckyI5gYRjFQWS5IN7c45u6Xa+fiMGtZIjEGO5++AADIradpsKbKZwzXVwh3NHNUsEsg2qUYXz/wcHLpYgoP1qz6vXKlsUIp2ErjPcWyKvgutrv3dnkzWvfWfZWgCmkPIvvzcugPR8t8DK0l9E44yHFfjEx1n5/9UMqx6aPC2CGIh0rhtYo1DeWTYuyXqA1yTYGgDQWJXM3JZChsfWztuNUVg2bSsHT7xxXuOqPS8caIk2ZzI1maqnbFHHe7s/Wmc+WhH6spdgoPM4Gf/8cm7Dw4zfFZvIUqQDaSpu+HtGrA2Atx/ztu498dTRn/nziqTOOm2f4/hpr6b3JxznSpNffvtv1ykVBDSH6rP2cOPzp37dPcZKQVo44orVsFnPyvnf7oqKU2ZLPvf5/vN5RRMMqwZ/ddYE+K1O6pnb0ic5st+9fuZL2PTwxOyJcWmQWfIBoIaPjle8v0DgFpZvmqIoH9V+bd07exZGYiN/PidNegqhq0rLR9gQST2sDArum2H7KgxAg2zWP/YPofemTWUrdSQzQUj3Gx9LJfFlQ6bcYTT4DI/m5oY3PLfKxwkCEH1usRopl36YAqNRpEi75BdX4vOlBKbtLHmKP5y/pdIUdajAxooKibcI1EiLFA2ii7RkKTBmfgw2kxJxVxA2Y0WR86fLyEwrurSv4JpBIit9Sm21KidUKAkUmCpYt1YSvoGErRBfvdVGa5I4OycS6ttjCo8Jq8RM8xPHoCzDFxoVSnJJIRASlTxnXXKJGAsHuy2gKNKWeDaWW0sEAwl4UByqTTlpiUVlxAHBsMmhyYrubOhef/iPVoJ1NKCNxwGhAZFxlRaTmyytPK3CosvXvAVySVNEQh0V99GOahLe2MP3kVoi86hJXmlNK59M++Olsk4xupLnnLma8flMmXfXYvOCuyE0eE+AOGRXuVkEL9mS+DBPhrSeDawIe688G2o/Ybf2nfR66xztjw6WiYV3DIqUVF4AgYy712yC91ZwIZmafdPKTBhx2FcEzQOmhGdDfOG7OI/OGMa7Il5TNLq3b5l9mxgW3TRQTL+8Yn9UlUVYuaGCbqU2TTEAhWmfjJPc0tZ23E2EzmO675Xxv2PMFClyGYp/pdSPT7wKHDH/56XudhR8D+jb2BtTcITU4psqBym7YYfvWUpovrGcjF9r2VQed5LNokF8JKUSWeBMRh3QyMmgIlTX08cCGsi28CW/WQ/pwjZQSmyWadjWH5xGSpGmQBp1tdslKkpSriDwVNUk0l1rJvrKDZgwmWunCRJNv2i43G7CN6oJBKyq3qujLOpjq2B6jB94xL/1H+7D/atdidkD6SNpDqiTDR1kGmULluKbMKK9I8WO1+AQJl19oSvdi7WKhbK7ev+qtCitOxkbCkTY1pYO2N8AxyrGAH1jelx/oNYn+pXhaHfxfdpnC4JNuaUIGuI9vNzyjIt787boPzqeU2ag6XkFF1JsFEOHXHy3IEZPi7NrGhJn4DHK87bjBE44+UVSoGNYJhBbtRrF+6GhCKSFtAMZQSDJvtFBNthTq692TRF/agEQs+n09KoFm28EqZi88UrcpxkRkti3tDGVjPQj1x1SNc71pIdBKUamXq0V+ilkV6HLQk2lZCVx3X/vsiiqJUtvwKXRjzQbWHinbm1rhTYOLdkIPSUm2uxxnChWhA2UjSy+/ap3nXC/kOhSVGxWYtpxuir85ujQUgBViOs//5m8OsILdcMOuOcNnuHPFgHQtBMO5F25OqkF2JdJ4qDzcSUxSgHiUlHBrXV9GX/sHtP93ROUVoHZsF5O+xR1UBBM/0OTYi6IZSKi7gY2LSsCw2ZfSZBRk7QbPgnvmDvaf+iU5YirpoxI+O4ShhD74IrLV0sjAqhffY8zpQNnDI6Ckj4vvInNxyEWpbf8Ex4ur/mtcwlHLeft9zXDNGfgWITnj1C6biB9qnFOFO2miChibK2iVPmkqIQK4js9Bsr5GkMnwsdvQ6dQTdzQIKBQKnQRIQoZBiYrLPFwMa1YqZpz7Qn7pi0dDdrUmkV7P/x2+Hpzm+AdIb7fVL71QVvZ7VJyLJsnTT2+ZcfGo9WciwKNmukApkd8fPVO5ZetES5tIWR4+pcHnEUhZw0e9IuuCjBetJTV3791duPrH/cpWk2VVGwOWekxdEjA4xHnVtudbT6J1vyqBfX5C+YE5Te1Q+8I0sTldjU2FsBamKTFQyKY97IeiiAEWMbke/+94XK6t73y+zpTQFpFPlEgATg4+/uot8joGLcJQtmPoiRVoktCh9AIUVWhHLclGrUq895QeK8HnsbEpJMd9rhf8QHW/Gw6wG0NRV3DS0ve4iibcnrimLe0ABjifv1bw/Ww8f/thZqznsG0o5mId/RyOCzge8pa5OqSaMRq46CFoLromCLjKNJGjGyQrkrrznIpv/HH+Y+OfPVuXOfz2vMffLxP8957qfdgTxezaTxgXVVn4C3mkXBltVoXMPwQVsX9h64w3xx7oQHfvubqffeOzWvce9dv541bewTN104lxRsdbfvP7707lEppnVcFDLp6DGSpHHRC1+9urIqC0Nv3FleW1t/oLouv1Fbkyn/MlX1ygVNQlRu2nXgwJd7kKVU+yxbnnE8yR3FFJonB2rTTr/fcwtgxFqhLkApei1mJt5W7qsUOLosGKlZZVHYScUpu2SIkoJJe/EjlGtqpmKTpyVxWicqCfHD83dFvjiIG24iNMURT1LEmysTodmLcUHfXZCzAq1Z3qHwzGB473UJJtyX0/iwuX1y1fbKu60FW3neK222Adv6zUdhoDjrlWs0jB56tO16+/SFFWCDoqwNBRXu/sEyF7Vx4qwrH/Qw6FosRjaKdodN3ed4G9lMFj/qtpPpoqwxdGbpBdt0uq2xEilaavgtDIOiZJMXP6LJEbRZYUxS1mONk8XIpubcuMOCbnOMa7kVD12ZKS59EzxX9njwhyuMxrit+gKc3P+uPm8pf3LHgiyKPCCSkfGFFZPHV1NC0PZ2CTaieOsvF6Yly+jQuaKIJ0OTGIfBmq4fU0wBbe/hAYJU9XD/6fyA1XUai4LNgdBaNw2hvBvTWou2PpSfKi5Xf3+ndjZpnyW8M9e3RCYGF/XfGShiE221k6BtghaD0dexvWSYGouDLTRaZfo8IR2PjJFtzZcdNxkAhlvOXaAc6LA42Ixz0bMDvkiUiJyK28wmgEvTBHLGhY7kwBbF+qQ2nB/u9oYz0kBim9psu8EJ5ZKjeGDgzATaKck5UzaltR31y4O5SgN3Rq2OiAc0uDd+WONAF8k+TuPqvstdezXncFg99D4ymrIY2LBJXTYti7y9NuOVWPuDvdKExcDG5Qf9PsWg3ep6VJSdeKNOF4ctqev7FytNu+XLJI2be7zZPqnOGevblGv3kVy2l0wSmmyc1yNdFGwbL3tTRipqL5k0kU5B+XVPFVYmc32Z0A76VVZryLbXWgDwjHHq9e7lx3yCKwgbMIofFb4x4BNMDLRbXQ8YEwZwaNIUZ7LCyVRB2LhpYBTb9r0/RmZZ3G52EqwNs3ZR7xWRpejU6EKwae3qOT7TdwtqYcP2K6m2GnmA1SMHm5BC5jN7ZW1lsxai1IGuLzqTWFDtVpBlOQgF2m25bCnJRSosCJtwKWl/fVMlSkvft32h5GRjQvNVm4Fnuzdxp40oBBu3Btf8cGWuDCsw2G59JXWdckwrfvD6R7WSJi4EGzPM9LmrEYBbwaH9Wp36UiEJqsGu+dFnjrnOtSU5CgDN5atXboPQKH8GON1ua6YO6Pex2GLNzffYE30b26bPrWbz5fG5HmiZnyzKyq8X29q5nNoHBXbjhe+Q1bS+GA4V6xQ2oP+R890eZl69G53pqBpxkWG/6alSIpTGWGdtZ7Bph8yfjMJ1lyxguVNuHTLAONjZ6znInU1ysm1WuLVsifZ9AkjJxo6qQYsdVdtvYsfg1XO/yh2kc0J1Cpvy/RwSg0svWwumA1t4A+lczfAxFlksbRvr0FvvA7ISBQT970kyArXqKDjDnXFrLvnQR2EWFe8MNgAyjhrn9d+KkbLQUT28bcLCgFXeeUOQ65Ghks5gU8rXy9f3eU6SngcddnwNDCgGsPryJSm/fQWmM9hA+e22add/lfsDdtgAX4zvonl9a1BkTeewIVNCVHZ/Dzt85GrxPvv5ky4dKNCdwWYdN+La+zIdz5ZzbeKFwdt9Yo+dwcaVs+9dUaZlB4M5PLYxXDtmnDFtC7laL5MZLq94JqU6uEmHLzSnMJzE8q99lpHV7BR90wEu6L/WHyjtWDY/Z74YFht/N4i1saa+tWwZnerxInRsj4ecTILLHWtxuO2ni9t4FCJ/NshtSlsYf10lue2OZrNWyWMn47LTbmjM+gSu1Y4gXzYLxpAXFWp7rwXeEXTW/Q0knF8O+YPV9DJ5qpVtDvNlI6OVFfRVXHZrgJZ12t0UlJnCk12r0RjNMWnoEDaT2JRvjTa/98cOYsNN56BZ4QQcGTLehkKlnBIdwoah1FZiw0WzfSmQsp108YaJwXJcdc4HyDhPWnlOJ182kArAuuk3bUZgxnTanSJOg1HRnX1Cdhgsa915xrxlEjRl9rt7vKQt+bYO928nXqkjE6ZgT78HIAitaN06c9520jpj1V2jv9QyFM7FnaZv2sT09ZUen2N9upXpYt4yqcjsrz9/BdYxTAvZSWhkn7MmJOdWOWaiMqyV9Zn5sjmMdDJocudeKPWN8fZFH9L7jTpE33xGOrvfRjAFYmuYMMLwVq6a5MtGDu1Iz99JcAViw7U9l5tWrp3nyyasu+cXB7BQ02aNfqRXhtKejmBD3HThm2gcFIZNx7h7wH2gOsR3o7xp4iHuZIEmDhwTr3bbgx0ik7js0nVh2Ll3QX5jOMGgctIw164+wNtH65vGXzs1cpDIArGpkFRtVfeVfgOCwrD8bMrp2IRlQUpIiv832ki7zoq1TlaJiDzs/QMCGTPRZPKbv9OxSQuH6iHVeMksCkdAFgqNoi0DuG3IHzFTgVa1z7wpSu0TgfdcvTcbOFUw7+as7xIupl/Z5Cjw4vnVM5/WliQRKHmwxxKsS3gH9WPKZ2iK9hTbMfQhykd4kt/i0OnYAJuYkmPGVwAKBRleMLYELDm5Fy74XKAQ+YVHp2PTuinE13p+gtLEhjFTIDsJ0sg0Kl138whfGKeT9mCDWMng0oel5SG3TJoCaRwZaLKUcYgreq0nL8DEmbDlZh28M1H46MCdyGPHSRoKFU/mVtF1aCD7UN8sZqrxTNg0RSD+ogZjcH+313zJVpGMrf2fwHTNGfk3HxQ7bfza9T0TDodJsaA5/kCPoyiCM2HL/R7j1yfKfvwOpmSxsHF5YNAv84wqW2b7unVieOOtdRgXCxvwEJd2W4PyTNjA2mOLSnP6fEKezUJxsFltddOvRgWpM2HzPSF9oXf9lY9y25AoWxxs6K/QKev1zBnJ5LHScYHTh32BnDtTLHaSU0CZ3NP3DG2JNRTl7L98lj/VpHSRsPkrXg18cc0ffRmDN+NtmjenYmvkxPEHgSvkpjjQ0PeDNALnXnoUhI3jb+/L3BJbLhHFFQNfcf50erGYEhoyBgEVN/9SigRPs/XRokxGiQujYeOagCRTgysSOAAVoxb4ctdVmLGnKU1tWd8Chs/1KUMfllIOXyR20p/1QM2gbsKYUETw7QfBW9Q3lTX1PR9DlwgAoYpl3gzzFpxkcf0l832j0bbNW1XGTB26n7IAyuGlLBZ986tuubP/4d1X1WEi2qZv9XLDBe9g6O8BlshUkbD5k9+5PoG49/oHkZlWyWSufN03/Uc5fHglWK6RaRRFEytr5qvYvOl/6fJDRvFcBbo1ebFROCIleh/yRtcP0RSP7f/H4axumHKLU5QwOw0ttCw+ic1fMUcvIgl/OllhsYQjJ0+fSmwuH3DWxqIFX9DlpBdiPJrBWb02oRLFCmekUcHd16YCMnaMtXBvxEn65vehKF071PNRxKxiojjZNNfCbe3/NEoOuTKNvOYNNM2ydZNuPgA2UUnRGMhmj8m1SSVPDKhAKUCJU/fibM6Wu0tVuh0D/urvpoiKxj42HzZJh3ho8HDumNQttBZpzmYgYiiz426v1mGigqRI9c2ZKK0TnHf+x0gxszz1HsxJ+mYTzvGt7u8j81c4qGJJbpqzSYNxE9bfPSExzEDC82LTPM7U/OzBYpXFZuOjS5djwr1dz8uWBCmc/vO9JcKWfWjEQQYtWLyTfDc5wn39nsdiDUiajw2XPktGM8yLjWyOGTqk3hbLutbp9C79+5FfkanMy5ZgjO/2eLN4g61mw7jKYbdTQM/yYhN110zNFM3yfx7juV6bUeQVc0mce8V61LJE5o1i+6rbx4jT2RJvR52RTTf9NsAkW6R+7aShOa7svgwVTdyx27JPweYsF77+Hx+/dg9paKkIpTFW8HGXx4HgGa7UP543Oc5m/UXoYYDlvWcjMF0iaKhCneh1vecipo/6mopTyyRNJyBLxg0vTyARrlT0jacVx7mXHdahcrbZGvGJefNXIwa4+L/fhzTKpGgXE5oNpym0ZwfHTlL1qIXRp2TThktIVV1zR2LRKiFLxHdbpYyqkq9fXKaklZydWiYxEyA+MOgQMk1ZW8BKg40mS9c2YcMt13FpVbNl5uNsoFiE5QNmYZwRPFS8SPPtk2RSOdI46z7uvdCXHZ+kb8aXoMmEB/CbEeUQkK1JeGmQ+Wf3NFbg/X3SzO8WAJhjV4ySBekCoLjRWoJQm/q86G9x83v4rlQGfP116zWzQCnFHc2k821nQYouOQMpNRiUw+4wUKLDwYrB27iyYUKeQOeueTSsCxgufM8CiW/8c7+nHn14ekmOaTN+9a8j/QmX2CrtBCdjz0UXdMzfsB0Y9fqEMb8YfcvQkhzDRoyc+EoQshh9P1WTaPrHdPFZqIqVYv5y9FKJRk7tDlIpQ5NmHOSyT9BddKJs9kjq8OaQTIwQxpbkEOmoMeuOXe+CLvHXWPKki1YxE19Mm/Hha3O+QJ1If87N+s8Tg7511n/6j0IP/wTWN0fyD+kf9djzgotiaWTZojUr1lVqScbEMtklRK2wouvt0ev9bqtBBzLxzTv/3gQYfA1H4q+L7MD2QHkPf7oPrEqc30XT9KnJt+XevcqmYNnYp99dPGWBzvWuBOzCrXa2YcB0gGcv2YZGsySVkd+oUdfkQURjjLEA5UShU1YissYXd5JbRplOVBiSZ06DjGWk1/zwScpllrxGsL74U3fBILS26eqhW1748f1kZWLMlFUeXbvseGWpxdX3T9lk1n3pm3sDKzQbaIkNh7IbVm/cVmEgqkeRlH+YgWxFZJy8rVu5Tps45fy14U6pLjyrwKUGD/7kD12nVgitDr28MSn/y7iNx19U7bN3TVgPL81JKa0LeEDguBQxdej9fat+MfmWUYuNt334+V1Dxv0ttXJlqCtHD6lClQGSUkU+QGIXZVGZ6j4zEN/7t9mC4YNTswl+NPmz47/t8TEfgGSHJ3/gbKKh0AVCShz+/XLc8Mrm2SP+5o0CP/rawqV9+jUdengZpn/ZY7dmkbYUVeZCR58HKKy79DGApf/0O3RNVz2FDbjk1q3HheDNsec8HIQ4anrOnBR+tWHx1ZlsIHHDlMj3k8NyetC3hteZZ8dIfOa/1qKEIM7dQAFouvi2bLbs4hs3LRo8YaPApZcvQWs/uHPL39V37v+8aWH4+LS3RwXPWRtvG4NpGwbzH0fub+21NhQLF2Iye8CXbv+N1+yD9J5aylglSmW7+NJ7s+uVP//tT3NilPhW/yWo7ZKJx2VSUiL3wNwI7r32K3IZhc/qdl/3AHKO2x7ZrfyFCjwG3PX8YYWLf7bB4ZbbZ65YtYcpoTXZUoonj60CHRNAwG2XLzJZfPeuz/3WN7kzfynkn5c14MO37UlctvC73/tuvc+ZBN99AJk1iZMB1L67j577nYFvOY1i3crdEapjU6CaryvXD/wTpT/P91uiyhd9QdELLpi//KUKjjdOa+IYK1loJ9B0x2R64+Hz8ymgyFBcrHY8+vzK97bjwis+tdhsteCk/YCJE7Imu/6PG+ThGUuqYy6fe2F5FeVCv3iWXgR3YcE3wOcNJtt3aOF+VbdkTqR47czr77zt/hV43xV+VRy/lc3tuH+ja/Q+u2HOquqaOOuviU/hp/MryWNEuvB1yxvuK09cZr9V1bMfijSr2vLRyvVbReqxORRcNOs80pwt63a+l44Zt+LQqqMmjJVLUjo4uLYWMwwFK/iypU1teC+VNcC127XTHjtLT7Zy9QdpMnRGfitbnDXbyzFILGGwWIVkiMihV6RQZ5RvnFhoNoNNmwPyb1zFlTym152VjsKsXXXIXPMT2iftCYc8CW0iWGQwK20mYUFKUhrrrWacFHxFlpKbgDvwYSVnGFPuKYXwJdUy9kHLt+ubTIT2LWYkoywoCbTVkVaB8DeQu1AUvDDP+auTtGb0IYArEWsfYtokDCNNT/qPrexOrueiMO3YTod0mtiU/wY9G+Yu+yzwxPnCV+23gI20BGJsrkuZM4r8AVGrb2M7m8b/s5Xm+D9CWLh1Q9UkNAAAAABJRU5ErkJggg==)
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=
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAABmADqQAGaQAGa2OgAAOjoAOmZmOma2OpDbZjoAZjpmZrbbZrb/kDoAkDo6kGaQtmYAtmY6tv//25A625Bm29uQ2////7Zm/9uQ//+2///bTz76BgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NggAMZYVYQW4yDG0wzMIjip2WEWCRAqhiBgAthDAEWSDUQEK0eSaEUGx+IJyPADqZFeflBtCSnDIiW5hGR4ecVhDiHkRmsECzPwCDOxiRCyD4Am1IDVcQqJDwAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Therefore, D and E are two points on side AB and AC respectively such that they divide side AB and AC in a ratio of 1:3
Coordinates of point D = (
)
= (
,
)
Coordinates of point E = (
,
)
= (
,
)
Area of the triangle =
[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 - y2)
=
[4 (
–
) +
(
- 6) +
(6 –
)]
=
[3 –
+
]
=
[
]
= 15/32 square units
Area of triangle ABC = [4 (5 – 2) + 1 (2 - 6) + 7 (6 – 5)] /2
= (12 – 4 + 7)/ 2
= 15/2 square units
Clearly, the ratio between the areas of ΔADE and ΔABC is 1:16
We know that if a line segment in a triangle divides its two sides in the same ratio, then the line segment is parallel tothe third side of the triangle.
These two triangles so formed (here ΔADE and ΔABC) will be similar to each other.
Hence, the ratio between the areas of these two triangles will be the square of the ratio between the sides of these two triangles
And, ratio between the areas of ΔADE and ΔABC = (1/4)2
= 1/16
Question 7.Let A (4, 2), B(6, 5) and C (1, 4) be the vertices of Δ ABC
(i) The median from A meets BC at D. Find the coordinates of the point D
(ii) Find the coordinates of the point P on AD such that AP: PD = 2: 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1
(iv) What do you observe?
[Note: The point which is common to all the three medians is called the centroidand this point divides each median in the ratio 2: 1]
(v) If
and
are the vertices of Δ ABC, find the coordinates of the centroid of the triangle
Answer:(i) Median AD of the triangle will divide the side BC in two equal parts
Therefore, D is the mid-point of side BC
![](data:image/png;base64,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)
And according to midpoint formula, midpoints of (x1, y1), (x2, y2) is given by
![](data:image/png;base64,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)
Coordinates of D = (
)
= (
)
(ii) Point P divides the side AD in a ratio 2:1
By section formula if (x, y) divides line joining points A(x1, y1), B(x2, y2) in ratio m:n
then,
![](data:image/png;base64,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)
Coordinates of P = (
)
= (![](data:image/png;base64,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)
(iii) Median BE of the triangle will divide the side AC in two equal parts.
Therefore, E is the mid-point of side AC
Coordinates of E = (
,
)
= (
)
Point Q divides the side BE in a ratio 2:1
By section formula if (x, y) divides line joining points A(x1, y1), B(x2, y2) in ratio m:n
then,
![](data:image/png;base64,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)
Coordinates of Q = (
)
= (![](data:image/png;base64,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)
Median CF of the triangle will divide the side AB in two equal parts. Therefore, F is the mid-point of side AB
Coordinates of F = (
)
= (5,
)
Point R divides the side CF in a ratio 2:1
By section formula if (x, y) divides line joining points A(x1, y1), B(x2, y2) in ratio m:n
then,
![](data:image/png;base64,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)
Coordinates of R = (
)
= (
)
(iv) It can be observed that the coordinates of point P, Q, R are the same.Therefore, all these are representing the same point on the plane i.e., the centroid of the triangle
(v)
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)
Consider a triangle, ΔABC, having its vertices as A(x1, y1), B(x2, y2), and C(x3,y3)
Median AD of the triangle will divide the side BC in two equal parts. Therefore, D is the mid-point of side BC
Coordinates of D = (
,
)
Let the centroid of this triangle be O. Point O divides the side AD in a ratio 2:1
By section formula if (x, y) divides line joining points A(x1, y1), B(x2, y2) in ratio m:n
then,
![](data:image/png;base64,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)
Coordinates of O = (
)
Centroid of ABC = (
)
Question 8.ABCD is a rectangle formed by the points A(–1, –1), B(– 1, 4), C(5, 4) and D(5, – 1). P, Q,R and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateralPQRS a square? a rectangle? or a rhombus? Justify your answer
Answer:P is the mid-point of AB
![](data:image/png;base64,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)
Coordinates of P = (-1,
)
Similarly coordinates of Q, R and S are (2, 4), (5,
) and (2, -1) respectively
Length of PQ = [(-1 – 2)2 + (
)2]1/2
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Length of QR = [(2 – 5)2 + (
)2]1/2
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Length of RS = [(5 – 2)2 + (
+ 1)2]1/2
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Length of SP = [(2+ 1)2 + (-1 –
)2]1/2
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Length of PR = [(-1- 5)2 + (
–
)2]1/2
= 6
Length of QS = [(2 – 2)2 + (4 + 1)2]1/2
= 5
It can be observed that all sides of the given quadrilateral are of the same measure. However, the diagonals are ofdifferent lengths. Therefore, PQRS is a rhombus
Determine the ratio in which the line divides the line segment joining the points A (2, – 2) and B (3, 7)
Answer:
Let the given line divide the line segment joining the points A(2, - 2) and B(3, 7) in a ratio k : 1
Coordinates of the point of division = ()
This point also lies on 2x + y - 4 = 0
Therefore,
2 () + (
) – 4 = 0
= 0
9k – 2 = 0
k =
Hence, the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A(2, - 2) and B(3, 7) is 2:9.
Question 2.
Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear
Answer:
If the given points are collinear, then the area of triangle formed by these points will be 0
Area of the triangle = [x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)
= [x (2 – 0) + 1 (0 – y) + 7 (y – 2)
0 = (2x – y + 7y – 14)
2x + 6y – 14 = 0
x + 3y – 7 = 0
This is the required relation between x and y
Question 3.
Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3)
Answer:
The figure for the question is:
Let O (x, y) be the centre of the circle. And let the points (6, - 6), (3, - 7), and (3, 3) be representing the points A, B,and C on the circumference of the circle
By distance formula, Distance between two points A(x1, y1) and B(x2, y2) is
AB = √((x2 - x1)2 + (y2 - y1)2)
Then,
OA = √[(x- 6)2 + (y+ 6)2]
OB = √[(x- 3)2 + (y+ 7)2]
OC = √[(x- 3)2 + (y- 3)2]
As OA, OB and OC are radii of same circle, OA = OB
[(x - 6)2 + (y + 6)2]1/2 = [(x - 3)2 + (y + 7)2]1/2
-6x – 2y + 14 = 0
3x + y = 7 (i)
Similarly, OA = OC
[(x - 6)2 + (y + 6)2]1/2 = [(x - 3)2 + (y - 3)2]1/2
-6x + 18y + 54 = 0
-3x + 9y = -27 (ii)
On adding equation (i) and (ii), we obtain
10y = - 20
y = - 2
From equation (i), we obtain
3x - 2 = 7
3x = 9
x = 3
Therefore, the centre of the circle is (3, - 2)
Question 4.
The two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of the other two vertices
Answer:
Let ABCD be a square having ( - 1, 2) and (3, 2) as vertices A and C respectively. Let (x, y), (x1, y1) be the coordinate of vertex B and D respectively
We know that the sides of a square are equal to each other
And also we know that for two points P(x1, y1) and Q(x2, y2), The distance between points P and Q is given by the formula
PQ = √(x2 - x1)2 + (y2 - y1)2
From the figure,
AB = BC
Therefore,
√[(x + 1)2 + (y - 2)2] = √[(x - 3)2 + (y - 2)2]
x2 + 2x + 1 + y2 – 4y + 4 = x2 + 9 – 6x + y2 + 4 – 4y
8x = 8
x = 1
We know that in a square, all interior angles are of 90°.
Pythagoras theorem : the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.In ΔABC,
Applying pythagoras theorem we get,AB2 + BC2 = AC2
√[(x + 1)2 + (y - 2)2] 2 + √[(x - 3)2 + (y - 2)2] 2 = √[(3 + 1)2 + (2 - 2)2] 2
4 + y2 + 4 - 4y + 4 + y2 - 4y + 4 =16
2y2 + 16 - 8 y =16
2y2 - 8 y = 0
y(y - 4) = 0
y = 0 or 4
Now we have obtained the B(x, y) point and we are left to find point C(x1, y1)We know that in a square, the diagonals are equal in length and bisect each other at 90°.
Let O be the mid-point of AC. Therefore, it will also be the mid-point of BD
If O is mid-point of AC, thenwe know, mid-point of (x1, y1) and (x2,y2) is
i.e.
therefore, O = (1, 2)
Also, if we take O as midpoint of BD then
Therefore, The sides of square are A(-1, 2), B(1, 4), C(1, 0) and D(3, 2)
or A(-1, 2), B(1, 0), C(1, 4) and D(3, 2)
Question 5.
The Class X students of asecondary school inKrishinagarhave been allotteda rectangular plot of land fortheir gardening activity.Sapling of Gulmohar areplanted on the boundary at adistance of 1m from each other.There is a triangular grassylawn in the plot as shown inthe Fig. 7.14. The students areto sow seeds of floweringplants on the remaining area of the plot
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?
Answer:
(i) Taking A as origin,
We will take AD as x-axis and AB as y-axis.
It can be observed that the coordinates of point P,Q, and R are (4, 6), (3, 2), and (6, 5) respectively
Area of the triangle PQR = [x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)
= [4 (2 – 5) + 3 (5 – 6) + 6 (6 – 2)
= (-12 – 3 + 24)
= Square units
(ii) Taking C as origin, CB as x-axis, and CD as y-axis, the coordinates of vertices P, Q, and R are (12, 2), (13, 6),and (10, 3) respectively
Area of the triangle PQR = [x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 - y2)
= [12 (6 – 3) + 13 (3 – 2) + 10 (2 – 6)
= (36 + 13 – 40)
= Square units
It can be observed that the area of the triangle is same in both the cases
Question 6.
The vertices of a Δ ABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that Calculate the area of theΔ ADE and compare it with the area of Δ ABC (Recall Theorem 6.2 and Theorem 6.6)
Answer:
Given that,
=
=
Therefore, D and E are two points on side AB and AC respectively such that they divide side AB and AC in a ratio of 1:3
Coordinates of point D = ()
= (,
)
Coordinates of point E = (,
)
= (,
)
Area of the triangle = [x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 - y2)
= [4 (
–
) +
(
- 6) +
(6 –
)]
= [3 –
+
]
= [
]
= 15/32 square units
Area of triangle ABC = [4 (5 – 2) + 1 (2 - 6) + 7 (6 – 5)] /2
= (12 – 4 + 7)/ 2
= 15/2 square units
Clearly, the ratio between the areas of ΔADE and ΔABC is 1:16
We know that if a line segment in a triangle divides its two sides in the same ratio, then the line segment is parallel tothe third side of the triangle.
These two triangles so formed (here ΔADE and ΔABC) will be similar to each other.
Hence, the ratio between the areas of these two triangles will be the square of the ratio between the sides of these two triangles
And, ratio between the areas of ΔADE and ΔABC = (1/4)2
= 1/16
Question 7.
Let A (4, 2), B(6, 5) and C (1, 4) be the vertices of Δ ABC
(i) The median from A meets BC at D. Find the coordinates of the point D
(ii) Find the coordinates of the point P on AD such that AP: PD = 2: 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1
(iv) What do you observe?
[Note: The point which is common to all the three medians is called the centroidand this point divides each median in the ratio 2: 1]
(v) If and
are the vertices of Δ ABC, find the coordinates of the centroid of the triangle
Answer:
(i) Median AD of the triangle will divide the side BC in two equal parts
Therefore, D is the mid-point of side BC
And according to midpoint formula, midpoints of (x1, y1), (x2, y2) is given by
Coordinates of D = ()
= ()
(ii) Point P divides the side AD in a ratio 2:1
By section formula if (x, y) divides line joining points A(x1, y1), B(x2, y2) in ratio m:nthen,
Coordinates of P = ()
= (
(iii) Median BE of the triangle will divide the side AC in two equal parts.
Therefore, E is the mid-point of side AC
Coordinates of E = (,
)
= ()
Point Q divides the side BE in a ratio 2:1
By section formula if (x, y) divides line joining points A(x1, y1), B(x2, y2) in ratio m:nthen,
Coordinates of Q = ()
= (
Median CF of the triangle will divide the side AB in two equal parts. Therefore, F is the mid-point of side AB
Coordinates of F = ()
= (5, )
Point R divides the side CF in a ratio 2:1
By section formula if (x, y) divides line joining points A(x1, y1), B(x2, y2) in ratio m:nthen,
Coordinates of R = ()
= ()
(iv) It can be observed that the coordinates of point P, Q, R are the same.Therefore, all these are representing the same point on the plane i.e., the centroid of the triangle
(v)
Consider a triangle, ΔABC, having its vertices as A(x1, y1), B(x2, y2), and C(x3,y3)
Median AD of the triangle will divide the side BC in two equal parts. Therefore, D is the mid-point of side BC
Coordinates of D = (,
)
Let the centroid of this triangle be O. Point O divides the side AD in a ratio 2:1
By section formula if (x, y) divides line joining points A(x1, y1), B(x2, y2) in ratio m:n
then,
Coordinates of O = ()
Centroid of ABC = ()
Question 8.
ABCD is a rectangle formed by the points A(–1, –1), B(– 1, 4), C(5, 4) and D(5, – 1). P, Q,R and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateralPQRS a square? a rectangle? or a rhombus? Justify your answer
Answer:
P is the mid-point of AB
Coordinates of P = (-1, )
Similarly coordinates of Q, R and S are (2, 4), (5, ) and (2, -1) respectively
Length of PQ = [(-1 – 2)2 + ()2]1/2
=
Length of QR = [(2 – 5)2 + ()2]1/2
=
Length of RS = [(5 – 2)2 + (+ 1)2]1/2
=
Length of SP = [(2+ 1)2 + (-1 – )2]1/2
=
Length of PR = [(-1- 5)2 + (–
)2]1/2
= 6
Length of QS = [(2 – 2)2 + (4 + 1)2]1/2
= 5
It can be observed that all sides of the given quadrilateral are of the same measure. However, the diagonals are ofdifferent lengths. Therefore, PQRS is a rhombus