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

The region represented by x-y≤2 and x+y≤2 is bounded by a
  1. rhombus of area 82 sq. units.
  2. rhombus of side length 2 units.
  3. square of area 16 sq. units.
  4. square of side length 22 units.

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--21+1=42=22

Asked in: JEE Main 2019 (10 Apr Shift 1)

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