Single correct option
What is the area of the region in the xy-plane defined by |x| + |2y| ≤ 6?
- A. 18
- B. 24
- C. 36
- D. 72
Show answer and solution
Answer: (C) 36
The boundary |x| + 2|y| = 6 is a rhombus with vertices where one variable is zero: (±6, 0) and (0, ±3).
Its diagonals are 12 (along the x-axis) and 6 (along the y-axis).
Area = ½ × 12 × 6 = 36.
Alternative: in the first quadrant it is a right triangle with legs 6 and 3 (area 9); four quadrants give 36.
Its diagonals are 12 (along the x-axis) and 6 (along the y-axis).
Area = ½ × 12 × 6 = 36.
Alternative: in the first quadrant it is a right triangle with legs 6 and 3 (area 9); four quadrants give 36.
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