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Find the ratio in which the point $(-1, k)$ divides the line segment joining the points $(-3, 10)$ and $(6,-8)$. Hence, find the value of $k$.
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Let $C (-1, k)$ be divides the line segment joining the points $A (-3, 10)$ and $B (6, -8)$ in the ratio $m : 1$.
Using section formula
$-1 = \frac{-3+6m}{m+1}$
$\Rightarrow m = \frac{2}{7}$
Hence, required ratio is $2 : 7$
$k = \frac{10\times7-8\times2}{2+7} = 6$
Using section formula
$-1 = \frac{-3+6m}{m+1}$
$\Rightarrow m = \frac{2}{7}$
Hence, required ratio is $2 : 7$
$k = \frac{10\times7-8\times2}{2+7} = 6$