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

Show Answer

Solution:

  1. 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.



NCERT Chapter Video Solution

Dual Pane