Let P and Q be the points of trisection of the line segment joining the points A (2, - 2) and B (- 7, 4) such that P is nearer to A. find the coordinate of P and Q.

As P and Q are the points of trisection so

AP = PQ = QB

consider

PB = PQ + PB

PB = AP + AP

PB = 2AP

i.e. P divides line joining the points A and B in a ratio 1 : 2

now we know that the coordinates of the points P(x, y) which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂), internally in the ratio m : n are

In this case we have

A(x₁, y₁) = (2, - 2)

B(x₂, y₂) = (- 7, 4)

m : n = 1 : 2

P(x, y) = (- 1, 0)

Now,

PQ = QB

i.e Q is the mid point of PB

[ As The mid - point of the line segment joining the points (x₁, y₁) and (x₁, y₁) is  

Coordinates of P = (- 1, 0) and