Question

Find the value of $a$, for which point $P(\frac{a}{3},2)$ is the mid-point of the line segment joining the points $Q(-5,4)$ and $R(-1,0)$.

Answer 1

Coordinates of midpoint are $(x,y)$

$x=\frac{(x_1+x_2)}{2}$

$y=\frac{(y_1+y_2)}{2}$

According to the question:

$x=\frac{-5-1}{2}=-3$

$\Rightarrow \frac{a}{3}=-3$

$\Rightarrow a=-9$

$y=\frac{(4+0)}{2}=2$

coordinate of mid point $=(-3,2)$
so, $a=-9$