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Q.
The midpoint of the line joining the points $ (-10,\text{ }8) $ and $ (-6,12) $ divides the line joining the points $ (4,-2) $ and $ (-2,4) $ in the ratio
The midpoint of the line joining the points $ (-10,8) $ and $ (-6,12) $ is $ \left( \frac{-10-6}{2},\frac{8+12}{2} \right) $ ie, $ (-8,10) $ . Let $ (-8,10) $ divides the line joining the points $ (4,-2) $ and $ (-2,4) $ in the ratio $ m:n $ .
$ \therefore $ $ \frac{m(-2)+n(4)}{m+n}=-8 $
$ \Rightarrow $ $ -2m+4n=-8m-8n $
$ \Rightarrow $ $ 6m=-12n $
$ \Rightarrow $ $ \frac{m}{n}=\frac{-2}{1} $
$ \therefore $ $ (-8,10) $ divides the line joining the points $ (4,-2) $ and $ (-2,4) $ in the ratio $ 2:1 $ externally.