Question

# ABCD is a quadrilateral. E is the point of intersection of the line joining the midpoint of the opposite sides. If O is any point and −−→OA+−−→OB+−−→OC+−−→OD=x−−→OE, then x is equal to

A
3
B
9
C
7
D
4

Solution

## The correct option is D 4Let −−→OA=→a, −−→OB=→b, −−→OC=→c and −−→OD=→d Therefore, −−→OA+−−→OB+−−→OC+−−→OD=→a+→b+→c+→d Let P, is the midpoint of AB, =→a+→b2  Let Q, is the midpoint of CD, =→c+→d2 Therefore, the midpoint of −−→PQ is →a+→b+→c+→d4 Similarly, the midpoint of −−→RS is →a+→b+→c+→d4 ⇒−−→OE=→a+→b+→c+→d4 ⇒x=4

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