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Point $P(x, 0)$ divides the line segment joining the points $(2, 8)$ and $(-3, -5)$ in a certain ratio. Find the ratio and hence find the value of $x$.
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Solution: Let $AP : PB = k : 1$ therefore $0 = \frac{-5k + 8}{k + 1} \Rightarrow k = \frac{8}{5}$ [1 1/2 marks]
Hence required ratio is $8 : 5$
$x = \frac{-24 + 10}{13} = -\frac{14}{13}$ [1/2 mark]
Hence required ratio is $8 : 5$
$x = \frac{-24 + 10}{13} = -\frac{14}{13}$ [1/2 mark]