Question

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

• A. 4
• B. -6
• C. -8
• D. -12

Answer 1

The correct option is D -12

The co-ordinates of the mid-point of the line segment joining the point $P(x_1,y_1),Q(x_2,y_2)$$=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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

$\Rightarrow (\frac{a}{3},4)=(\frac{-8}{2},4)$

X co-ordinates

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

$\Rightarrow a=\frac{-8\times 3}{2}=-12$