Single correct option
What is the area of the triangle formed by the lines y = 2x, y = −2x and y = 8?
- A. 32
- B. 24
- C. 40
- D. 16
Show answer and solution
Answer: (A) 32
The vertices are:
- y = 2x and y = −2x meet at (0, 0).
- y = 2x and y = 8 meet at (4, 8).
- y = −2x and y = 8 meet at (−4, 8).
Base (along y = 8) from x = −4 to x = 4 has length 8. Height = 8 (from the origin up to y = 8).
Area = ½ × 8 × 8 = 32 square units.
Tip: Lines y = ±mx with y = k always make a triangle of area k²/m.
- y = 2x and y = −2x meet at (0, 0).
- y = 2x and y = 8 meet at (4, 8).
- y = −2x and y = 8 meet at (−4, 8).
Base (along y = 8) from x = −4 to x = 4 has length 8. Height = 8 (from the origin up to y = 8).
Area = ½ × 8 × 8 = 32 square units.
Tip: Lines y = ±mx with y = k always make a triangle of area k²/m.
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