Question

Question 13
If $P(\frac{a}{3},4)$ is mid-point of the line segment joining points Q(-6,5) and R(-2,3), then value of a is
(A) – 4
(B) – 12
(C) 12
(D) – 6

Answer 1

Given that, $P(\frac{a}{3},4)$ is the mid-point of the line segment joining points Q(-6,5) and R(-2,3), which is shown in the figure given below:

$\therefore \text{Mid-point of QR}=P(\frac{-6-2}{2},\frac{5+3}{2})=P(-4,4)\left[\begin{array}{c}\text{Since, mid-point of line segment joining the points}\\ (x_1,y_1)and(x_2,y_2)\\ =(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\end{array}\right]\text{But it is given that mid-point is}P(\frac{a}{3},4)\therefore (\frac{a}{3},4)=(-4,4)\text{On comparing the coordinates, we get}\frac{a}{3}=-4\therefore a=-12\text{Hence, the required value of a is - 12.}$