Question

If point P divides segment AB in the ratio 1 : 3 where A(– 5, 3) and B(3, – 5), then the coordinates of P are ______

Options

• (– 2, – 2)

• (– 1, – 1)

• (– 3, 1)

• (1, – 3)

Answer 1

(– 3, 1)

Let A(x₁, y₁) = A(-5, 3) and B(x₂, y₂) = B(3, -5),

a : b = 1 : 3

∴ x₁ = -5, y₁ = 3, x₂ = 3, y₂ = –5, a = 1, b = 3.

∴ By section formula,

∴ x = `(ax_2 + bx_1)/(a + b)` ∴ x = `(1(3) + 3(-5))/(1 + 3)` ∴ x = `(3 - 15)/(4)` ∴ x = `(- 12)/(4)` ∴ x = -3

∴ y = `(ay_2 + by_1)/(a + b)` ∴ y = `(1(-5) + 3(3))/(1 + 3)` ∴ y = `(-5 + 9)/(4)` ∴ y = `(4)/(4)` ∴ y = 1

∴ Co-ordinates of P are (-3, 1).