Area Bounded by Absolute Value Equation

CAT 2017 Slot 1 · QA · Easy · Co-ordinate Geometry

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The area of the closed region bounded by the equation ∣x∣+∣y∣=2|x| + |y| = 2 in the two-dimensional plane is

  1. A.

    4π4\pi

  2. B.

    4

  3. C.

    8

  4. D.

    2π2\pi

Answer

C

Explanation

The equation ∣x∣+∣y∣=2|x| + |y| = 2 forms a square with vertices at (2,0),(0,2),(−2,0),(2, 0), (0, 2), (-2, 0), and (0,−2)(0, -2). The diagonal length is 44. Area of the square = 12×d1×d2=12×4×4=8\frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times 4 \times 4 = 8.

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