In what ratio does the point P (2, – 5) divide the line segment joining A (– 3,5) and B(4, – 9)?

Question

Philoid · Accepted Answer

Let the point P (2, – 5) divide the line segment joining A (– 3,5) and B(4, – 9) in the ratio m:n.

Let (x,y) ≡ (2, – 5)

(x₁,y₁) ≡ (– 3,5)

and (x₂,y₂) ≡ (4, – 9)

Using Section Formula,

⇒ 2 × (m + n) = 4m – 3n

⇒ 2m + 2n = 4m – 3n

⇒ 5n = 2m

∴ m:n = 5:2

Since the ratio is positive, Point P divides the line segment AB internally in the ratio 5:2.