Question

In what Ratio the line joining (– 1, 1) and (5, 7) is divided by the line x + y = 4?

Answer 1

Let the points be A(x₁, y₁) = (– 1, 1) and B(x₂, y₂) = (5, 7) and P(x₃, y₃) be the point which divides AB in the ratio m: n.

∴ Co-ordinates of P are \(\big(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}\big)\)

= \(\big(\frac{5m - n}{m + n}, \frac{7m + n}{m + n}\big)\)

Since the point P lies on line x + y = 4.

∴ \(\frac{5m - n}{m + n}, \frac{7m + n}{m + n}\) = 4

⇒ \(\frac{12m}{m+n}\) = 4

⇒ 8m = 4n

⇒ m: n = 1: 2.