Question

The co-ordinates of P and Q are $(3,a+3)$ and $(a+6,6)$. The mid point of PQ is $(2,2)$, then $a$ is

• A. $3$
• B. $-2$
• C. $0$
• D. $-5$

Answer 1

Answer: (D)

$-5$

Mid point of two points ${(x}_1,y_1)$ and ${(x}_2,y_2)$ is calculated by the formula $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
Given, midpoint of $PQ=(2,2)$
$=>(\frac{3+a+6}{2},\frac{a+3+6}{2})=(2,2)$
$=>\frac{9+a}{2}=2;\frac{a+9}{2}=2$
$=>9+a=4$
$=>a=-5$