Question

The vertices of $\Delta PQR$ are $P(2,1),Q(-2,3)$ and $R(4,5)$. Find equation of the median through the vertex $R$.

Answer 1

Let $L$ be the mid-point of $PQ$.
Thus by mid-point formula, the coordinates of point $L$ is given by,
$(\frac{2-2}{2},\frac{1+3}{2})=(0,2)$
Therefore, the equation of $RL$ (median through vertex $R$) is given by,
$(y-5)=\frac{2-5}{0-4}(x-4)$
$\Rightarrow y-5=\frac{-3}{-4}(x-4)$
$\Rightarrow 4(y-5)=3(x-4)$
$\Rightarrow 4y-20=3x-12$
$\Rightarrow 3x-4y+8=0$