Question

In the given figure, line APB meets the x-axis at point A and y-axis at point B. P is the point (−4, 2) and AP : PB = 1 : 2. Find the co-ordinates of A and B.

Answer 1

Given, A lies on x-axis and B lies on y-axis.

Let the co-ordinates of A and B be (x, 0) and (0, y) respectively.

Given, P is the point (−4, 2) and AP : PB = 1 : 2.

Using section formula, we have:

`-4 = (1 xx 0 + 2 xx x)/(1 + 2)`

`-4 = (2x)/3`

`x = (-4 xx 3)/2 = -6`

Also,

`2 = (1 xx y + 2 xx 0)/(1 + 2)`

`2 = y/3`

`y = 6`

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