Question

The line AB intersects x-axis at A and y-axis at B. The point P(2, -3) lies on AB such that AP : PB = 3 : 1. Find the co-ordinates of A and B.

Answer 1

Given AP : PB = 3 : 1

Using section formula

X = `(x_1m_2 + x_2m_1)/(m_1 + m_2)`

Y = `(y_1m_2 + y_2 m_1)/(m_1 + m_2)`

X, Y is a coordinate of P(2, −3)

Let coordinate of A(x₁, 0) and coordinate of B(0, y₂)

m₁ = 3, m₂ = 1

2 = `(x_1 xx 1 + 3 xx 0)/(3 + 1)`

8 = `x_1/4`

x₁ = 8

−3 = `(3 xx y_2 + 0 xx 1)/(3 + 1)`

−3 = `(3y_2)/4`

−3 × 4 = 3y₂

y₂ = −4

Co-ordinate of A (8, 0)

Co-ordinate of B (0, −4)