Question

Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.

Answer 1

Distance between two points (x₁, y₁) ( x₂, y₂) is:

d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

Distance between A(–3, –14) and B(a, –5) is:

d = `sqrt([(a + 3)^2 + (-5 + 14)^2])` = 9

Squaring on L.H.S and R.H.S.

(a + 3)² + 81 = 81

(a + 3)² = 0

(a + 3)(a + 3) = 0

a + 3 = 0

a = –3