The area bounded by the curve \( |-x|+|-y|=2 \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 8 sq. units
Since \( |-x|=|x| \) and \( |-y|=|y| \), the curve is \( |x|+|y|=2 \). In the first quadrant it is the line x + y = 2, and the curve is symmetric about both axes.
So the curve is a square with vertices (2, 0), (0, 2), (−2, 0) and (0, −2). Its diagonals are each 4 units long.
\( \displaystyle \text{Area}=\frac{1}{2}\times d_1\times d_2 \)
\( \displaystyle =\frac{1}{2}\times 4\times 4 \)
\( \displaystyle =8\ \text{sq. units} \)
Why the other options are incorrect
Option (1) 2 sq. units — Incorrect. This is the area of only the first-quadrant part, a triangle of area ½ × 2 × 2 = 2. The whole curve has four such parts.
Option (2) 4 sq. units — Incorrect. The area is 8, not 4.
Option (3) 6 sq. units — Incorrect. The area is 8, not 6.