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CAT 2022 Slot 1 Paper

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Question : 62 of 66

Marks: +1, -0

Let $ABCD$ be a parallelogram such that the coordinates of its three vertices $A,B, C$ are $E(1, 1), (3, 4)$ and $(-2, 8)$ respectively. Then,the coordinates of the vertex $D$ are

$(0,11)$
$(4,5)$
$(-3,4)$
$(-4,5)$

Solution:

In a parallelogram, two diagonals of parallelogram bisects each other, which concludes that mid-point of both diagonals are the same.

Midpoint of

AC = \left( \frac{1-2}{2}, \frac{1+8}{2} \right)

Let the coordinates of vertex

D

be

(x, y)

\left( \frac{x+3}{2}, \frac{y+4}{2} \right) = \left( \frac{1-2}{2}, \frac{1+8}{2} \right)

x = -4

and

y = 5

The answer is option D.

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