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The vertices of $\triangle P Q R$ are $P(2,1), Q(-2,3)$ and $R(4,5)$. Find equation of the median through the vertex $R$.
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Verified Answer
The middle point of $P Q$ is $S=\left(\frac{2-2}{2}, \frac{1+3}{2}\right)$ or $(0,2)$
$\therefore$ Equation of the median $R S$ where $R$ is $(4,5)$ and $S$ is the point $(0,2)$ is
$y-5=\frac{2-5}{0-4}(x-4)$
or $y-5=\frac{-3}{-4}(x-4)$
or $\quad 4(y-5)=3(x-4)$
or $4 y-20=3 x-12$
i.e. $3 x-4 y=-8$
$\therefore$ Equation of median $R S$ is $3 x-4 y+8=0$
$\therefore$ Equation of the median $R S$ where $R$ is $(4,5)$ and $S$ is the point $(0,2)$ is
$y-5=\frac{2-5}{0-4}(x-4)$
or $y-5=\frac{-3}{-4}(x-4)$
or $\quad 4(y-5)=3(x-4)$
or $4 y-20=3 x-12$
i.e. $3 x-4 y=-8$
$\therefore$ Equation of median $R S$ is $3 x-4 y+8=0$
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