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JEE Main 201910 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
10 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2019 · 10 April · Morning Shift · Mathematics · Area Under Curves

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

The region represented by ∣x−y∣≤2and∣x+y∣≤2\left|x - y\right| \le 2 and \left|x + y\right| \le 2 is bounded by aThe region represented by |x - y| ≤ 2 and |x + y| ≤ 2 is bounded by a

Options

  1. Arhombus of area 82sq.units8\sqrt{2}sq . units.
  2. Brhombus of side length 22 units.
  3. Csquare of area 16sq.units16sq . units.
  4. Dsquare of side length 222\sqrt{2} units.

Correct answer

D. square of side length 222\sqrt{2} units.

Step-by-step solution

\left|x + y\right| = 2 ⇒ x + y = 2andx+y=–2</p><p>∣x–y∣=2⇒x–y=2and x + y = – 2</p><p>\left|x – y\right| = 2 ⇒ x – y = 2 and x – y = – 2

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

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=2andx+y=−2x + y = 2 and x + y = - 2

=∣2−(−2)∣1+1=42=22= \dfrac{\left|2 - \left(- 2\right)\right|}{\sqrt{1 + 1}} = \dfrac{4}{\sqrt{2}} = 2\sqrt{2}

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