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ISI2020-MMA: 1

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Let $\text{A} = (1, -1), \text{B} = (-2, 0), \text{C} = (1, 2)$ and $\text{D}$ be the vertices of a parallelogram in the $\text{X – Y}$ plane listed clockwise. Then the point $\text{D}$ is

  1. $(4, 1)$

  2. $(-2, -3)$

  3. $(3, 0)$

  4. $(-2, 1)$

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Let the three vertices of parallelogram ABCD be A(1,-1),B(-2,0) and C(1,2)

Let the fourth vertex be D(a,b)

By joining AC and BD intersect at point O

i.e, diagonals of parallelogram bisect each other.

Mid point of AC= ( (1+1)/2, (-1+2)/2 ) = (1,1/2)

Mid point of BD=( (x-2)/2, (y+0)/2 )

So, (x-2)/2 = 1   =>   x=4

y/2 = 1/2   =>   y=1

∴x=4,y=1

∴ The coordinate of fourth vertex =(4,1) ☺
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