UPSC NDA Math Model Paper 4

For x < 0, y = -x - 1 and y = x + 1
y = -x - 1, when x = 0, y = -1 ⇒ (0, -1) and when y = 0, x = -1 ⇒ (-1, 0)
And y = x + 1, when x = 0, y = 1 ⇒ (0, 1) and y = 0, x = -1 ⇒ (-1, 0)
For x > 0, y = x - 1 and y = -x + 1
y = x - 1, when x = 0, y = -1, (0, -1) and when y = 0, x = 1 ⇒ (1, 0)
And, y = -x + 1, when x = 0, y = 1, (0, 1) and when y = 0, x = 1 ⇒ (1, 0) We get square, now length of side = distance between any two points
Consider points (1, 0) and (0, 1)
Distance =√(1−0)2+(0−1)2=√2
Area of square =(√2)2
= 2 sq units
Hence, option (3) is correct.