Question

Find the distance between each of the following pairs of points. 

i. A (2, 3), B (4,1) 

ii. P (-5, 7), Q (-1, 3) 

iii. R (0, -3), S (0, 5/2)

Answer 1

i. Let A (x₁ , y₁ ) and B (x₂ , y₂ ) be the given points. 

∴ x₁ = 2, y₁ = 3, x₂ = 4, y₂ = 1 

By distance formula,

∴ d(A, B) = 2 units 

∴ The distance between the points A and B is 2 units. 

ii. Let P (x₁ , y₁ ) and Q (x₂ , y₂ ) be the given points. 

∴ x₁ = -5, y₁ = 7, x₂ = -1, y₂ = 3 By distance formula,

∴ d(P, Q) = 4∴ d(P, Q) = 4√2  units  

∴ The distance between the points P and Q is 4√2units.

iii. Let R (x₁ , y₁ ) and S (x₂ , y₂ ) be the given points. 

∴ x₁ = 0, y₁ = -3, x₂ = 0, y₂ = By distance formula,

∴ d(R, S) = -y units 

∴ The distance between the points R and S is 11/2 units.