CAT 2022 Slot 1 QA Question 21: 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

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

For a parallelogram ABCD with vertices in order, the diagonals bisect each other. Equivalently,
$A + C = B + D$
$\Rightarrow D = A + C - B$
$D = (1,1) + (-2,8) - (3,4)$
$D = (1-2-3, 1+8-4)$
$D = (-4,5)$
Answer: (2) $(-4, 5)$

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

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