question_answer

If P and Q are the points on the line joining A (-2, 5), B (3, 1) such that AP = PQ = QB. then the mid-point of PQ is:

A)  \[\left( \frac{1}{2},3 \right)\]      

B)  \[\left( -\frac{1}{2},4 \right)\]

C)  \[(2,3)\]            

D)  \[(-1,3)\]

Correct Answer: A

Solution :

(a): If we consider AP = PQ = QB, then, K is simply the mid-point of AB. \[\therefore \] \[K=\left( \frac{-2+3}{2},\frac{5+1}{2} \right)=\left( \frac{1}{2},3 \right)\]