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If (-1,2),(2,-1) and (3,1) are any three vertices of a parallelogram, then
(a) a=2, b=0
(b) a=-2, b=6
(c) a=-2, b=0
(d) a=6, b=2

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Hi Prateek, let D(a,b) be the fourth vertex of parallelogram
Let A(-1,2) B(2,-1) and C(3,1) 
Slope of AB = (-1-2)/(2+1) = -1
Slope of CD = (b-1)/(a-3)
As AB and CD are parallel, their slopes are equal.
Hence b - 1 = - a + 3
OR a + b = 4 ---(1)
Now slope of AD = (b-2)/(a+1)
Slope of BC = (1+1)/(3-2) = 2
Again the slopes are equal we have b -2 = 2a + 2
==> 2 a - b = - 4 ----(2)
Solving (1) and (2) we ge a = 0 and b = 4
Hence D(0,4) has to be the fourth vertex. But such an option is missing. Please check your data once again
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