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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.

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#### Solution

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

Concept: Section Formula

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