Question

In XY-plane, area bounded by $|x+y| + |x-y| = 4$:

• A. 8
• B. 12
• C. 16
• D. 20

Hint:

Use rotation transformation to simplify absolute value equations.

Answer 1

The Correct Option is C

Transform $u = x+y$, $v = x-y$. Equation becomes $|u| + |v| = 4$, a diamond in $uv$-plane with area = $2(4)^2 = 32$. But scaling from $u,v$ back to $x,y$ divides area by 2: $16$. \[ \boxed{16} \]