SATHEE: Straight Line and Pair of Straight Lines 1 Question 4

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 $8 \sqrt{2} s q$ units

(d) square of area $16 s q$ units

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Solution:

The given inequalities are

$| x - y | \leq 2 and | x + y | \leq 2 .$

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.

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Straight Line and Pair of Straight Lines 1 Question 4

4. The region represented by |x−y|≤2 and |x+y|≤2 is bounded by a

Solution:

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4. The region represented by $| x - y | \leq 2$ and $| x + y | \leq 2$ is bounded by a