Area Under the Curve
Area bounded by piecewise linear curves
Grade 12

Question:

<p>Area enclosed by the curve \(|x + y - 1| + |2x + y + 1| = 1\) is</p>
<p>(A) 2 sq. units</p>
<p>(B) 1 sq. unit</p>
<p>(C) 4 sq. units</p>
<p>(D) none of these</p>

Step-by-Step Solution

Key Concept: Absolute value equations define piecewise linear regions; find vertices by solving boundary conditions and compute area.
<p>Analyze the condition $|x + y - 1| + |2x + y + 1| = 1$ by considering different regions based on the signs of the linear expressions. This defines a region (typically a quadrilateral). Calculate vertices and use the shoelace formula or decomposition to find the area = 2 sq. units.</p>
Correct Answer: A

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