# 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:**

Reasoning:

The distance between the two points can be measured using the distance formula which is given by:

Distance Formula = √ [(x_{2 - }x_{1})^{2} + (y_{2} - y_{1})^{2}]

(i) Let the points be A(2, 3) and B(4, 1)

Therefore, x_{1} = 2, y_{1} = 3, x_{2} = 4, y_{2} = 1

We know that the distance between the two points is given by the distance formula

Distance Formula = √[(x_{2 - }x_{1})^{2} + (y_{2} - y_{1})^{2}]

Therefore, the distance between A(2, 3) and B(4, 1) is given by

d = √[(4_{ - }2)^{2} + (1 - 3)^{2}]

= √4 + 4

= √8

= 2√2

(ii) Distance between (- 5, 7) and (- 1, 3) is given by

d = √[( -1 +^{ }5_{ })^{2} + (3 - 7)^{2}]

= √16 + 16

= √32

= 4√2

(iii) Distance between (a, b) and (- a, - b) is given by

d = √[(-a -^{ }a)^{2} + (-b - b)^{2}]

d = √[(-2a)^{2} + (-2b)^{2}]

d = 2 √(a^{2} + b^{2})

**Video Solution:**

## Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (- 5, 7), (- 1, 3) (iii) (a, b), (- a, - b)

### NCERT Class 10 Maths Solutions - Chapter 7 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)

The distance between the pair of points (2, 3), (4, 1) is 2√2 and between points (- 5, 7), (- 1, 3) is 4 √2 and between points (a, b), (- a, - b) is d = 2 √ ( a^{2} + b^{2})