Question:
The area of the closed region bounded by the equation \(| x | + | y | = 2\) in the two-dimensional plane is
The area of the closed region bounded by the equation \(| x | + | y | = 2\) in the two-dimensional plane is
Updated On: Sep 26, 2024
- \( 4\pi\)
- 4
- 8
- \( 2\pi\)
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The Correct Option is C
Solution and Explanation
The area enclosed by the equation \(∣ax∣+∣by∣=c\) in the two-dimensional plane is \(±\frac{c}{|a|}\) and y- intercepts of \(±\frac{c}{|b|}\)
In general, it forms a rhombus. However, in the given scenario, we have a square with diagonals each measuring 4 units.
Area \(= \frac{1}{2}(4)(4)=8\)
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