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

$M$ is the midpoint on the line segment $PQ$ since $RM$ is the median.

$\therefore$ Co-ordinates of $M$ can be found using the midpoint theorem

$=(\frac{2-2}{2},\frac{3+1}{2})=(0,2)$

$\therefore$ Equation of line $RM$ is

$y-2=\frac{2-5}{0-4}\left(x\right)$

$\Rightarrow Y-2=\frac{+3}{+4}x$

$\Rightarrow 4y-8=3x$

$\Rightarrow 3x-4y+8=0$