The co-ordinates of two points A and B are ( – 3, 3) and (12, – 7) respectively. P is a point on the line segment AB such that AP : PB = 2 : 3. Find the co-ordinates of P.

Solution:

Let the co-ordinates of P(x, y) divides AB in the ratio m:n.

A(-3,3) and B(12,-7) are the given points.

Given m:n = 2:3

x₁ = -3 , y₁ = 3 , x₂ = 12 , y₂ = -7 , m = 2 and n = 3

By Section formula x = (mx₂+nx₁)/(m+n)

x = (2×12+3×-3)/(2+3)

x = (24-9)/5

x = 15/5

x = 3

By Section formula y = (my₂+ny₁)/(m+n)

y = (2×-7+3×3)/5

y = (-14+9)/5

y = -5/5

y = -1

Hence the co-ordinate of point P are (3,-1).