JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Straight Lines

The region represented by

∣ x - y ∣ \leq 2

and

∣ x + y ∣ \leq 2

is bounded by a:

(A)rhombus of area $82$ sq. units
(B)square of area 16 sq. units
(C)rhombus of side length 2 units
(D)square of side length $22$ units✓ Correct

Answer: (D)

Solution

The conditions

∣ x - y ∣ \leq 2

and

∣ x + y ∣ \leq 2

unfold to

- 2 \leq x - y \leq 2

and

- 2 \leq x + y \leq 2

, four lines bounding a square tilted at

4 5^{\circ}

with corners at

(2, 0)

(0, 2)

(- 2, 0)

and

(0, - 2)

. Two adjacent corners are

(2 - 0)^{2} + (0 - 2)^{2} = 8 = 22

apart, so the region is a square of side

22

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option

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