CAT 2022 Slot 1 QA Question & Solution

GeometryMedium

Question

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

Options

(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.