Question

A line AB meets the x-axis at point A and y-axis at point B. The point P(−4, −2) divides the line segment AB internally such that AP : PB = 1 : 2, Find:

(i) the co-ordinates of A and B

(ii) equation of line through P and perpendicular to AB.

Answer 1

(i) Let the co-ordinates of point A (lying on x-axis) be (x, 0) and the co-ordinates of point B (lying y-axis) be (0, y).

Given, P = (−4, −2) and AP : PB = 1 : 2

Using section formula, we have:

Thus, the co-ordinates of A and B are (−6, 0) and (0, -6).

Required equation of the line passing through P and perpendicular to AB is given by