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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.
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
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