Question

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

Answer 1

In $△PQR$,

$P=(2,1)$

$Q=(-2,3)$

$R=(4,5)$

Mid-point of $PQ=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{2-2}{2},\frac{1+3}{2})=(0,2)$

Equation of the median through the vertex $R$ is the equation of the line passing through the points $(0,2),(4,5)$

Since, two points form of the line is $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)(x-x_1)$

$\therefore$ Equation of the median is

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

$⟹4(y-2)=3x$

$⟹4y-8=3x$

$3x-4y+8=0$ (Ans)