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

Here P(2, 1), Q(-2, 3) and R(4, 5) are the vertices of $\Delta PQR$.

RS is the median through vertex R.

Then S is mid point of PQ.

$\therefore$ Coordinates of S are $(\frac{2-2}{2},\frac{1+3}{2})$ i.e. (0, 2)

So equation of required median RS is

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

$\Rightarrow y-2=\frac{3}{4}x\Rightarrow 4y-8=3x$

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