Find the distance between the following pairs of points :
(i) (2, 3), (4, 1) 

(ii) (– 5, 7), (– 1, 3)

 (iii) (a, b), (– a, –b)

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 √(a² + b²)