Question

What will be the absolute value of $a$, for which point $P\left(\frac{a}{2},2\right)$ is the mid-point of the line segment joining the point $Q\left(-5,4\right)$ and $R\left(-1,0\right)$

Answer 1

Given, $QR$ is a line segment and $P$ is unit-point of $QR$.

So,

Let $x=\frac{a}{2}$&$y=2$

$\because (x,y)$ is unit-point of $(-5,4)$ & $(-1,0)$

$\therefore y=\frac{4+0}{2}=2$

$\therefore x=\frac{-5+(-1)}{2}=\frac{-6}{2}=-3$

$\because x=\frac{a}{2}=-3$

$\Rightarrow a=-3\times 2=-6$