Question

Line 4x + y = 4 divides the line segment joining the points (−2, −1) and (3, 5) in a certain ratio. Find the ratio.

Answer 1

Let the line 4x + y = 4 intersects AB at P(x₁, y₁) such that AP: PB=k:1 

 x₁= 3k−2/k+1 and y₁= 5k−1/k+1 

(x₁, y₁) lies on 4x + y = 4 

Therefore, 4(3k−2/k+1)+(5k−1/k+1) = 4 

 ⇒ k = 1 

 The required ratio is 1:1