Question

Determine the ratio in which the line x – y – 2 = 0 divides the line segment joining the points A(3, -1) and B(8, 9) 

Answer 1

Let the Line x – y – 2 = 0

divides the line segment joining the point A (3, -1) and B (8, 9) at point P (x, y) in the ratio λ : 1.

⇒ 8λ + 3 – 9λ + 1 = 2(λ + 1)

⇒ -λ + 4 = 2λ + 2

⇒ 3λ = 2

⇒ λ = 2/3

⇒ λ : 1 = 2 : 3

Hence, required ratio 2 : 3.