CAT 2022 Slot 1 QA Q1 Coordinate Geometry

Question 1 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

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
  1. A
    (−4, 5)
  2. B
    (4, 5)
  3. C
    (−3, 4)
  4. D
    (0, 11)

Answer: (A) (−4, 5) Coordinate Geometry MCQ

Solution

  1. In a parallelogram ABCD the diagonals bisect each other, so \(A + C = B + D\).
  2. \(D = A + C - B = (1 - 2 - 3,\ 1 + 8 - 4) = (-4, 5)\).

Shortcut. Fourth vertex opposite B is always \(A + C - B\).

Same concept in other years

See every question on Parallelogram diagonals bisect each other: share a midpoint.

More Coordinate Geometry questions from CAT

All 16 Coordinate Geometry questions asked since 2017.