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Question

If (7,3), (6,1), (8,2) and (p,q) are the vertices of a parallelogram, taken in order, then the value of p is
  1. 9

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Solution

The correct option is A 9
The point of intersection of the diagonals bisect the diagonals in a parallelogram

First diagonal is formed by the points (7,3) and (8,2).

Point of intersection of the diagonals is the mid point of this diagonal.

Hence, the point of intersection is (7+82,3+22) = (152,52)

Now, the other diagonal is formed by the points (6,1) and (p,q).

The mid point of this diagonal is (6+p2,1+q2)

The point of intersection of the two diagonals is the same point

Hence, 6+p2=152
6+p=15p=9

and, 1+q2=52
1+q=5q=4

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