These NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 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.

Solution:

Question 2.

Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).

Solution:

Let P (x_{1}, y_{1}) and Q (x_{2}, y_{2}) be the points of trisection of A (4, -1) and B (- 2, – 3).

Therefore, P divides AB internally in the ratio of 1.2. Therefore, by section formula coordinates of P are

Now, Q also divides AB internally in the ratio 2 : 1, so the coordinates of Q are

Therefore, the coordinates of the points of trisection of the line segment joining A and B are (2, \(\frac { 5 }{ 3 }\)) and (0, \(\frac { 7 }{ 3 }\))

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 1 m from each other along AD, as shown in given figure below. Niharika runs \(\frac { 1 }{ 4 }\) the distance AD on the 2nd line and posts a green flag. Preet runs \(\frac { 1 }{ 5 }\) th 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?

Solution:

If the position of Niharika be M and the position of Preet by N the coordinate of point M are (2, 25) and the coordinate of point N are (8, 20) Distance between M and N are

Rashmi has to post a blue flag exactly halfway between the line MN. Suppose this point is 0. Then O divides the line MN at the ratio 1 :1

So, the coordinate of point O (x_{1}, x_{2})

The coordinate of O are (5, 22.5)

∴ The position of the blue flag is 5th line at a distance of 22.5 m

Question 4.

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).

Solution:

Let the required ratio be k : 1

Question 5.

Find the ratio in which 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.

Solution:

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.

Solution:

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).

Solution:

Question 8.

If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = \(\frac { 3 }{ 7 }\) AB and P lies on the line segment AB.

Solution:

Question 9.

Find the coordinates of the points which divide the line segment joining A (-2, 2) and B (2, 8) into four equal parts.

Solution:

Question 10.

Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.

[Hint: Area of a rhombus = \(\frac { 1 }{ 2 }\) (product of its diagonals)]

Solution: