Single correct option
What is the area of the triangle formed by the lines x + y = 6, x − y = 2 and the y-axis?
- A. 12 sq units
- B. 16 sq units
- C. 24 sq units
- D. 8 sq units
Show answer and solution
Answer: (B) 16 sq units
Vertices:
- x + y = 6 and x − y = 2 meet at (4, 2).
- x + y = 6 meets the y-axis at (0, 6).
- x − y = 2 meets the y-axis at (0, −2).
The side on the y-axis has length 6 − (−2) = 8; the height is the x-coordinate of (4, 2), i.e. 4.
Area = ½ × 8 × 4 = 16 sq units.
- x + y = 6 and x − y = 2 meet at (4, 2).
- x + y = 6 meets the y-axis at (0, 6).
- x − y = 2 meets the y-axis at (0, −2).
The side on the y-axis has length 6 − (−2) = 8; the height is the x-coordinate of (4, 2), i.e. 4.
Area = ½ × 8 × 4 = 16 sq units.
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