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KEAM 2016 Math Paper

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Question : 50 of 120

Marks: +1, -0

The points (-1, 0) and (-2, 1) are the two extremities of a diagonal of a parallelogram. If (-6, 5) is the third vertex, then the fourth vertex of the parallelogram is

(2, -6)
(2, -5)
(3, -4)
(-3, 4)
(3, -5)

Solution:

Let the points of parallelogram are

A(-2,1), B(-6,5)

C(-10)

and

D(x, y)

We know that, diagonals of parallelogram bisect each other.

\left(\frac{-2-1}{2},\;\frac{1+0}{2}\right)=\left(\frac{x-6}{2},\;\frac{y+5}{2}\right)

\;\frac{-3}{2}=\;\frac{x-6}{2}

and

\;\frac{1}{2}=\;\frac{y+5}{2}

\Rightarrow -3=x-6

and

1=y+5

\Rightarrow x=-3+6

and

y=1-5

\Rightarrow x=3

and

y=-4

Thus. coordinates of fourth vertex of parallelogram are

(3-4)

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