Question

If point P(1, 1) divide segment joining point A and point B(–1, –1) in the ratio 5 : 2, then the coordinates of A are ______.

Options

• (3, 3)

• (6, 6)

• (2, 2)

• (1, 1)

Answer 1

If point P(1, 1) divide segment joining point A and point B(–1, –1) in the ratio 5 : 2, then the coordinates of A are (6, 6).

Explanation:

Let A(x₁, y₁) and B(x₂, y₂) = B(–1, –1)

P(x, y) = P(1, 1) divides AB in ratio 5 : 2

∴ x₁ = 1, y₁ = 1, x₂ = –1, y₂ = –1, a = 5, b = 2

∴ By section formula,

`x = (ax_2 + bx_1)/(a + b)`

∴ `1 = (5(-1) + 2x_1)/(5 + 2)`

∴  7 = –5 + 2x₁

∴ 2x₁ = 7 + 5

∴ 2x₁ = 12

∴ `x_1 = 12/2`

∴ x₁ = 6

∴ Co-ordinates of A are (6, 6).