Question

If $A=(6,-7),B=(-6,5)$ and $P,Q$ are two points on $AB$ such that $AP=PQ=QB$, then which of the following is/are correct?

• A. $P=(2,3)$
• B. $P=(2,-3)$
• C. $Q=(2,-1)$
• D. $Q=(-2,1)$

Answer 1

Answer: (B), (D)

$Q=(-2,1)$

Given: $AP=PQ=QB$, $A=(6,-7),B=(-6,5)$


$\Rightarrow AP:PB=1:2\text{and}AQ:QB=2:1$

$P=(\frac{-6+12}{3},\frac{5-14}{3})=(2,-3)$
$Q=(\frac{6-12}{3},\frac{-7+10}{3})=(-2,1)$