Question

Prove that origin O divides the line joining the points 4(1, -3) and B(-3, 9) in the ratio 1 : 3 internally. Find the co-ordinates of the points which externally divides the line.

Answer 1

Let the point P(x, y) divides the line segment joining the point A(1, -3) and B(-3, 9) internally in the ratio 1 : 3.

Hence co-ordinate of P(x, y) is (0, 0). 

So origin O is divides the line segment joining the given points internally in the ratio 1 : 3.

Again point P(x, y) divides externally, then by formula of external division

Hence, co-ordinate of point P which divides externally = (3, -9).