Single correct option
What is the area enclosed by the curve |x| + |2y| = 8?
- A. 32
- B. 48
- C. 64
- D. 128
Show answer and solution
Answer: (C) 64
The curve is a rhombus with vertices where one variable is zero:
- y = 0 → x = ±8, giving (8, 0) and (−8, 0).
- x = 0 → |2y| = 8 → y = ±4, giving (0, 4) and (0, −4).
Diagonals are 16 and 8, so area = (1/2) × 16 × 8 = 64.
Why 128 is wrong: that is the product of diagonals without the 1/2. Why 32: it confuses |2y| = 8 with y = ±2.
Tip: |x|/a + |y|/b = 1 encloses a rhombus of area 2ab (here a = 8, b = 4).
- y = 0 → x = ±8, giving (8, 0) and (−8, 0).
- x = 0 → |2y| = 8 → y = ±4, giving (0, 4) and (0, −4).
Diagonals are 16 and 8, so area = (1/2) × 16 × 8 = 64.
Why 128 is wrong: that is the product of diagonals without the 1/2. Why 32: it confuses |2y| = 8 with y = ±2.
Tip: |x|/a + |y|/b = 1 encloses a rhombus of area 2ab (here a = 8, b = 4).
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