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 ______.

विकल्प

• (–2, –2)

• (–1, –1)

• (–3, 1)

• (1, –3)

Answer 1

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 (–3, 1).

Explanation:

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)` = `(1(3) + 3(-5))/(1 + 3)` = `(3 - 15)/(4)` = `(- 12)/(4)` ∴ x = –3

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

∴ Co-ordinates of P are (–3, 1).