cat 2022 Question 1

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

Accepted Answer

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

Midpoint of AC = ($\frac{1-2}{2}, \frac{1+8}{2}$)

Let the coordinates of vertex D be (x, y)

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

x = -4 and y = 5

The answer is option D.

Question 1.

Question Explanation