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Question:

If $P\left(\frac{a}{2}, 4\right)$ is the midpoint of the line segment joining the points $A(-6,5)$ and $B(-2,3)$ then the value of $a$ is

(a) $-8$

(b) 3

(c) $-4$

(d) 4

Solution:

The point $P\left(\frac{a}{2}, 4\right)$ is the midpoint of the line segment joining the points $A(-6,5)$ and $B(-2,3)$. So

$\frac{a}{2}=\frac{-6-2}{2}$

$\Rightarrow \frac{a}{2}=-4$

$\Rightarrow a=-8$

Hence, the correct answer is option (a).