Question

Find the distances between the following points. 

i. A (a, 0), B (0, a) 

ii. P (-6, -3), Q (-1, 9) 

iii. R (-3a, a), S (a, -2a)

Answer 1

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

∴ x₁ = a, y₁ = 0, x₂ = 0, y₂ = a 

By distance formula,

∴ d(A, B) = a√2 units

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

∴ x₁ = -6, y₁ = -3, x₂ = -1, y₂ = 9 

By distance formula,

∴ d(P, Q) = 13 units 

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

∴ x₁ = -3a, y₁ = a, x₂ = a, y₂ = -2a 

By distance formula,

∴ d(R, S) = 5a units