If the midpoint of the line segment connecting the points Q(- 6, 5) and R(- 2, 3) is $\mathrm{P}\left(\frac{\mathrm{a}}{3}, 4\right)$ then find the value of a.

We know, Mid-point of two points $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ and $\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)$ is calculated by the formula $\left(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2}\right)$

Given, the midpoint of $\mathrm{Q}(-6,5) \& \mathrm{R}(-2,3) is \mathrm{P}\left(\frac{\mathrm{a}}{3},4\right)$

On substitution, we get:

$\Rightarrow \left(\frac{-6-2}{2},\frac{5+3}{2}\right)=\left(\frac{\mathrm{a}}{3}, 4\right)$

Equating the x- axis coordinates, we get: 

$\Rightarrow \frac{-8}{2}=\frac{\mathrm{a}}{3}$

$\Rightarrow -24=2\mathrm{a}$

$\Rightarrow \mathrm{a} = -12$