Question

A point P divides the line segment joining the points A(3, –5) and B(–4, 8) such that `(AP)/(PB) = k/1`. If P lies on the line x + y = 0, then find the value of k.

Answer 1

It is given that `(AP)/(PB) = k/1`

So, P divides the line segment joining the points A(3, -5) and B(-4, 8) in the ratio k : 1.

Using the section formula, we get

Coordinates of P = `((-4k + 3)/(k + 1)"," (8k - 5)/(k + 1))`

Since P lies on the line x + y = 0, so

`(-4k + 3)/(k +1) + (8k - 5)/(k + 1) = 0`

`=> (-4k + 3 + 8k - 5)/(k + 1) = 0`

`=> 4k - 2 = 0`

`=> k = 1/2`

Hence, the value of k is `1/2`