Straight Line and Pair of Straight Lines 1 Question 4
4. The region represented by $|x-y| \leq 2$ and $|x+y| \leq 2$ is bounded by a
(2019 Main, 10 April I)
(a) rhombus of side length 2 units
(b) rhombus of area $8 \sqrt{2} sq$ units
(c) square of side length $2 \sqrt{2}$ units
(d) square of area $16 sq$ units
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Solution:
- The given inequalities are
$$ |x-y| \leq 2 \text { and }|x+y| \leq 2 . $$
On drawing, the above inequalities, we get a square
Now, the area of shaded region is equal to the area of a square having side length $\sqrt{(2-0)^{2}+(0-2)^{2}}=2 \sqrt{2}$ units.
