Question

$P$ and $Q$ are two points lying on the line joining the points $A(12,8)$ and $B(-2,6)$ such that $AP=PQ=QB.$ Then the midpoint of $PQ$ is

• A. $(7,1)$
• B. $(9,3)$
• C. $(6,4)$
• D. $(5,7)$

Answer 1

The correct option is D $(5,7)$


Let $O$ be the mid point of $PQ.$
It is given that $AP=PQ=BQ$
Hence, the midpoint of $PQ$ is same as the midpoint of $AB$, i.e. $O$

Therefore, coordinates of $O$ are
$O\equiv (\frac{12-2}{2},\frac{8+6}{2})\Rightarrow O\equiv (5,7)$