CAT 2000 — QA Question 44
BasicsEasy
The area bounded by the three curves |x + y| = 1, |x| = 1, and |y| = 1, is equal to
Answer & solution
Correct answer: 3
- A
4
3
- C
2
- D
1
Solution
We need to find area bounded by |x + y| = 1, |x| = 1, and |y| = 1
i.e. all points P(x, y) in the plane such that −1≤ x + y ≤ 1, −1≤ x ≤ 1, and −1≤ y ≤ 1
−1≤ x + y will be the origin side of line x + y = −1
x + y ≤ 1 will be the origin side of line x + y = 1
−1≤ x ≤ 1 will be the area between the lines x = −1 and x = 1.
−1≤ y ≤ 1 will be the area between the lines y = −1 and y = 1.
Tracing these curves, we get the area shown in the graph below
∴ Shaded Area = Area of 3 squares of side 1 unit = 3 × (1)2 = 3
Hence, option (b).