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Question 15 : The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is

1. 4π
2. 4
3. 8
4. 2π

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Coordinate Geometry

The area of the closed region bounded is given by the equation,
| x | + | y | = 2.
We can substitute x = 0 or y = 0.
The coordinates we obtain are as follows;
(2,2) , (-2,2) , (2,-2) and (-2,-2)
On joining these points you will get a square whose diagonal is 4 units. Therefore, the sides of the square will be 2√(2) and its area will be 2√(2) × 2√(2) = 8
The area of the closed region is 8 sq. units.

The question is "The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is"

Hence, the answer is 8 sq. units

Choice C is the correct answer.