Question

Find the coordinates of the point C, which lies on the line AB produced such that AC = 2BС, where the coordinates of points A and B are (–1, 7) and (4, –3), respectively.

Answer 1

Given AC = 2BC

∴ B is the midpoint of AС.

Coordinates of B = `((-1 + x)/2, (7 + y)/2)`

(4, −3) = `((-1 + x)/2, (7 + y)/2)`

`4 = (-1 + x)/2, -3 = (7 + y)/2`

8 + 1 = x, −6 − 7 = y

x = 9, y = −13

The coordinates of point C are (9, −13).