Question

The line joining $A (2, -7)$ and $B(6, 5)$ is divided into $4$ equal parts by the points $P,Q$ and $R$ such that $AQ = RP = QB$. The midpoint of $PR$ is _______

• A. (4,-1)
• B. (8,-2)
• C. (4,12)
• D. (-8,1)

Answer 1

Answer: (A)

(4,-1)

Answer 2

Given that,

$A P=P Q=Q R=R B$
and $A Q=R P=Q B$
Since, $A Q=Q B$, that means $Q$ is the mid point of
$A B=\left[\frac{2+6}{2}, \frac{-7+5}{2}\right]=(4,-1)$
Mid point of $P R=(4,-1)$
$[\because P Q=Q R]$