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GATE 2022 EC – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Four points P(0, 1), Q(0, −3), R(−2, −1), and S(2, −1) represent the vertices of a quadrilateral.

What is the area enclosed by the quadrilateral?

  1. 4
  2. $4\sqrt2$
  3. 8
  4. $8\sqrt2$

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Correct answer: (C) 8

Explanation

The diagonals PQ (along the $y$-axis) and RS (along the line $y=-1$) are perpendicular, with lengths $4$ and $4$. The area of a quadrilateral with perpendicular diagonals is $\frac12\times4\times4=8$.