Coordinate Geometry
Area of set defined by absolute value inequalities
MJMT_Full_Test_06
Grade 12
Question:
Area bounded by the set of points $S=\{(x,y):\,||x|-1|+||y|-1|\leq1\}$ is
Step-by-Step Solution
Key Concept: By symmetry in $x,y$ and their signs: in each quadrant the region is a diamond $|x-1|+|y-1|\leq1$ (area 2). The four quadrant diamonds share only boundary points.
Total area $=8$.
Correct Answer: 8