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JEE Main201910 Apr 2019Morning ShiftMathematicsArea Under CurvesActual

The region represented by x - y ≤ 2 and x + y ≤ 2 is bounded by a

Options

  1. Arhombus of area 8 2   sq .   units .
  2. Brhombus of side length 2 units.
  3. Csquare of area 16   sq .   units .
  4. Dsquare of side length 2 2 units.

Correct answer

D. square of side length 2 2 units.

Step-by-step solution

x + y = 2 ⇒ x + y = 2 and x + y = – 2 x – y = 2   ⇒ x   – y = 2 and x – y = – 2 So, the region bounded by the given curves, i.e., pairs of straight lines, is a square. Now, length of side of square = distance between parallel lines x + y = 2 and x + y = - 2 = 2 - - 2 1 + 1 = 4 2 = 2 2

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