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Question

If the points A(2,1),B(1,0),C(a,3) and D(1,b) form a parallelogram ABCD, find the value of a and b.

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Solution

In the parallelogram ABCD , AC and BD are the diagonals.

Co-ordinates of mid-point of AC=(2+a2,1+12)

Co-ordinate of mid-point of BD=(1+12,0+b2)

It is known that diagonals of the parallelogram bisect each other. Thus mid point of AC and BD coincide each other.

Thus,

2+a2=1a=4

1+12=b2b=2



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