Question

If $P(\frac{a}{3},4)$ is the mid-point of the line segment joining the points $Q(6,5)$ and $R(2,3)$, then the value of $a$ is

• A. $-4$
• B. $-12$
• C. $12$
• D. $-6$

Answer 1

The correct option is C $12$

$P\left(\frac{a}{3}.4\right)$ is the mid - point of the line segment joining $Q(6,5)$and $R(2,3)$.

Using section formula,

co-ordinates of $P=(\frac{6+2}{2},\frac{5+3}{2})$

co-ordinates of $P=(\frac{8}{2},\frac{8}{2})$

co-ordinates of $P=(4,4)$

$\frac{a}{3}=4$

$\Rightarrow a=12$