Let S be the set of all points (x, y) in the x-y plane such that | x | + | y | ≤ 2 and | x | ≥ 1. Then, the area, in square units, of the region represented by S equals
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Correct answer: C
Explanation
The correct answer is option 2 i.e. 2.
The possible values of |x| + |y| ≤ 2
x + y = 2
x - y = 2
y - x = 2
- y - x = 2
The possible values of |x| ≥ 1
x = 1 or -1
Area of the region X should be outside the (1, 0) and (-1, 0) and to be inside the (2 ,0) and (-2,0)
The area of shaded triangle = b(h)/2 = 2(1)/2 = 1 sq units
The Total area of shaded region = 2(area of triangle) = 2(1) = 2 sq units