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

Here given points are A (3, -5) and B (-4, 8) .

Let point P be (x, y) which divides AB in ratio of k:1, also point P lies on line x + y = 0

By section formula,

x = , y =

For point P on the line joined by the points A and B.

x = , y =

Putting in given equation,

+ =0

∴-4k +3 +8k -5 = 0

∴ 4k = 2

∴ k =