NCERT Solutions
Class 10 - Mathematics

Chapter 7: COORDINATE GEOMETRY

Find the distance between the following pairs of points:

1. (2, 3), (4, 1)
2. (−5, 7), (−1, 3)
3. (a, b), (−a, −b)

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?

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 triangle.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using the distance formula, find which of them is correct.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

1. (−1, −2), (1, 0), (−1, 2), (−3, 0)
2. (−3, 5), (3, 1), (0, 3), (−1, −4)
3. (4, 5), (7, 6), (4, 3), (1, 2)

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(10, y) is 10 units.

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.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).

Find the coordinates of the point which divides the join of (−1, 7) and (4, −3) in the ratio 2 : 3.

Find the coordinates of the points of trisection of the line segment joining (4, −1) and (−2, −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 Fig. 7.12. Niharika runs \(\tfrac{1}{4}\)th the distance AD on the 2nd line and posts a green flag. Preet runs \(\tfrac{1}{5}\)th 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?

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

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.

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

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).

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

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

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 \(= \dfrac{1}{2}\) × product of its diagonals.)