# NCERT solutions for class 10 Maths chapter 7 Coordinate Geometry (Exercise 7.1)

## Ex 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)

Solution:

## Ex 7.1 Question2.

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.

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## Ex 7.1 Question 3.

Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Solution:

## Ex 7.1 Question 4.

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Solution:

## Ex 7.1 Question 5.

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 distance formula, find which of them is correct.

Solution:

## Ex 7.1 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)

Solution:

## Ex 7.1 Question 7.

Find the point on the x-axis which is equidistant from (2, – 5) and (- 2, 9).

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## Ex 7.1 Question 8.

Find the values of y for which the distance between the points P (2, – 3) and Q (10, y) is 10 units.

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## Ex 7.1 Question 9.

If Q (0, 1) is equidistant from P (5, – 3) and R (x, 6), find the values of x. Also find the distance QR and PR.

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## Ex 7.1 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).

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