Single correct option
What is the area of the triangle with vertices (1, 2), (5, 5) and (−3, 8)?
- A. 18 sq units
- B. 15 sq units
- C. 24 sq units
- D. 36 sq units
Show answer and solution
Answer: (A) 18 sq units
Area = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
= ½ |1(5 − 8) + 5(8 − 2) + (−3)(2 − 5)|
= ½ |−3 + 30 + 9| = ½ × 36 = 18 sq units.
36 is the value before halving — the most common slip.
Check: vectors from (1,2): (4,3) and (−4,6); cross product = 4·6 − 3·(−4) = 36; half is 18 ✓.
= ½ |1(5 − 8) + 5(8 − 2) + (−3)(2 − 5)|
= ½ |−3 + 30 + 9| = ½ × 36 = 18 sq units.
36 is the value before halving — the most common slip.
Check: vectors from (1,2): (4,3) and (−4,6); cross product = 4·6 − 3·(−4) = 36; half is 18 ✓.
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