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Find the ratio in which point $P(-1, m)$ divides the line segment joining the points $A(2, 5)$ and $B(-5, -2)$. Hence, find the value of $m$.
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Let the required ratio be $k:1$
$-1 = \frac{-5k + 2}{k + 1}$ [$1$ mark]
$\Rightarrow k = \frac{3}{4}$ [$\frac{1}{2}$ mark]
$\Rightarrow$ ratio is $3:4$
$\Rightarrow m = 2$ [$\frac{1}{2}$ mark]
$-1 = \frac{-5k + 2}{k + 1}$ [$1$ mark]
$\Rightarrow k = \frac{3}{4}$ [$\frac{1}{2}$ mark]
$\Rightarrow$ ratio is $3:4$
$\Rightarrow m = 2$ [$\frac{1}{2}$ mark]