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 intersect 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.