Question

In the X – Y plane, the area of the region bounded by the graph of | x + y | + | x – y | = 4 is(2005)

• A. 8
• B. 12
• C. 16
• D. 20

Answer 1

The correct option is C 16

Let x ≥ 0, y ≥ 0 and x ≥ y

Then, | x + y | + | x – y | = 4

→ x + y + x – y = 4 → x = 2

And in case x ≥ 0, y ≥ 0, x ≤ y

x + y + y – x = 4 → y = 2

Area in the first quadrant is 4.

By symmetry, total area 4 × 4 = 16 unit.