Question

If $P(\frac{a}{3},4)$ is the mid point of the line segment joining the points $(-6,5),(-2,3).$ Then, find the value of $a.$

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

Answer 1

The correct option is B $-12$

$P(x,y)$ is md-point of $QR$ then

$(\frac{a}{3},4)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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

$\to \frac{a}{3}=\frac{-8}{2}$

$\Rightarrow a=-4\times 3=-12$

verifies the ans. (b)