# 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:**

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

Distance Formula = √ [(x₂_{ - }x₁)^{2} + (y₂ - y₁)^{2}]

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

Therefore, x₁ = 2, y₁ = 3, x₂ = 4, y₂ = 1

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

Distance Formula = √[(x₂_{ - }x₁)^{2} + (y₂ - y₁)^{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})

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 7

**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

**Summary:**

The distance between the following pairs of points (i) (2, 3), (4, 1) is 2√2 (ii) (- 5, 7), (- 1, 3) is 4 √2 and (iii) (a, b), (- a, - b) is 2 √ ( a^{2} + b^{2})

**☛ Related Questions:**

- 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 distance formula, find which of them is correct.

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