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Question

Three consecutive vertices of a parallelogram are (2,1),(1,0) and (4,3). Find the fourth vertex.

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Solution

Diagonals of a parallelogram bisect each other,
let the point of intersection of diagonals be M(m,n)

m=2+42=1 and n=1+32=1

m=1 and n=1

Let the Fourth vertex be D(x,y)

m=1+x2=1 and n=0+y2=1

x+1=2 and y=2

Thus x=1 & y=2

The fourth vertex of the parallelogram is D(1,2)

962703_973566_ans_f08b3e1de7864d6092caf5197bb1406a.png

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