ABCD is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opposition sides. If O is any point
and OA + OB + OC + OD = XOE, then x is equal to
(A) 3
(B) 9
(C) 7
(D) 4
Answers
Answered by
2
Step-by-step explanation:
Let
OA =a, OB = b, OC= c
and
OD= d
.
Therefore,
OA +OB+ OC+OD= a+ b+c + d.
The midpoint P of AB, is
2a+b
.
The position vector of the midpoint Q of CD, is
2c+ d.
Therefore, the position vector of the midpoint of PQ is
4a+ b + c+ d.
Similarly, the position vector of the midpoint of RS is
4a+ b+c+ d
, i.e.,
OE= 4a+ b+ c+ d
⇒x=4
Hence, option 'D' is correct.
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