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CAT 2016 Slot 1 · Quant · Coordinate Geometry · easy

What is the area (in square units) of the triangle with vertices (1, 2), (5, 6) and (7, −2)?

Single correct option

What is the area (in square units) of the triangle with vertices (1, 2), (5, 6) and (7, −2)?
  1. A. 18
  2. B. 20
  3. C. 22
  4. D. 24
Show answer and solution

Answer: (B) 20

Area = (1/2)|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

= (1/2)|1(6 + 2) + 5(−2 − 2) + 7(2 − 6)|

= (1/2)|8 − 20 − 28| = (1/2)(40) = 20.

Tip: Shift one vertex to the origin to simplify: vectors (4, 4) and (6, −4) give area (1/2)|4·(−4) − 4·6| = 20.
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Original question written in the CAT 2016 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake