Answer :

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(x_{1}, y_{1}) and B(x_{2}, y_{2}), internally in the ratio m : n are

In this case we have

A(x_{1}, y_{1}) = (2, - 2)

B(x_{2}, y_{2}) = (- 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 (x_{1}, y_{1}) and (x2, y2) is

Q = (-4, 2)

Coordinates of P = (- 1, 0) and Q = (-4, 2)

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