NCERT Solutions
Class 10 - Mathematics - Chapter 7: COORDINATE GEOMETRY

Exercise 7.1

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).