These NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1 Questions and Answers are prepared by our highly skilled subject experts.

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

Solution:

(i) Let P (2, 3) and Q (4, 1) be the two points. Therefore, by distance formula we know that

Therefore distance between points (2, 3) and (4, 11) is 2\(\sqrt{2}\) unit.

(ii) Let P (- 5, 7) and Q (- 1, 3) be two points.

Therefor by distance formula we know that

Therefore, distance between points (- 5, 7) and (- 1, 3) is 4\(\sqrt{2}\) unit.

(iii) Let P (a, b) and Q (-a, – b) be the points.

Therefore, by distance formula we know that

Therefore, distance between points (a. b) and (- a, – b) is 2\(\sqrt{a^{2}+b^{2}}\) unit.

Question 2.

Find the distance between the points (0, 0) and (36, 15).

Solution:

The distance between the points (0,0) and (36,15) by using distance formula, the distance of point P (x_{1}, y_{1}) from (0, 0) are

The distance between two towns is 39 km.

Question 3.

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

Solution:

Let points be A (1, 5), B (2, 3) and C (-2, -11)

Question 4.

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

Solution:

Let points be A(5, -2), B (6, 4) and C (7, -2)

Therefore, points (1,5), (2, 3) and (-2, -11) are not collinear.

Question 5.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in given figure. 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:

Points A (3, 4), B (6, 7), C (9, 4) and D (6, 1)

By distance formula we come to know that Champa is correct. The quadrilateral ABCD is a square

Because AB = BC = CD = DA = 3\(\sqrt{2}\)

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:

(i) Let points be A (-1, -2), B (1, 0), C (-1, 2) and D (-3, 0) be the vertices of quadrilateral.

Therefore, by distance formula, we know that

AB = BC = CD = AD and diagonals AC = BD

So, the quadrilateral formed by points (-1, -2), (1, 0), (-1,2) and (-3, 0) is a square.

(ii) Let A (-3, 5), B (3, 1), C = (0, 3) and D = (-1, -4) be the vertices of quadrilateral.

Therefore, by distance formula, we know that

There is no quadrilateral from the given points.

(iii) Let A (4, 5), B (7, 6), C (4,3) and D (1,2) be the vertices of quadrilateral ABCD.

Therefore, by distance formula, we know that

The points (4,5), (7,6), (4,3) and (1,2) form a parallelogram.

Question 7.

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

Solution:

Let P (x, 0) be a point on x-axis which is equidistant from the points. A (2, -5) and B (-2, 9)

Using the distance formula, we have

Hence, the required point on the x-axis is P (x, 0) = P (-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.

Solution:

By distance formula we know that

Therefore, the values of y are – 9 and 3

Question 9.

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

Solution:

By distance formula we know that.

According the question,

Now the points Q (0,1), P (5, -3) and R (4, 6) by using of distance formula.

Question 10.

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

Solution:

Let the points be P (x, y), Q (3, 6) and R (- 3, 4). By using distance formula.