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    Question

    What is the area of triangle ABC with vertices A(1, 2),

    B(5, 6), and C(7, 2)?
    A 12 Correct Answer Incorrect Answer
    B 18 Correct Answer Incorrect Answer
    C 10 Correct Answer Incorrect Answer
    D 24 Correct Answer Incorrect Answer

    Solution

    ATQ, Use the coordinate area formula: Area = (1/2) · |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. Let A(1,2) → (x₁,y₁), B(5,6) → (x₂,y₂), C(7,2) → (x₃,y₃). Compute: y₂ − y₃ = 6 − 2 = 4 y₃ − y₁ = 2 − 2 = 0 y₁ − y₂ = 2 − 6 = −4 x₁(y₂ − y₃) = 1 × 4 = 4 x₂(y₃ − y₁) = 5 × 0 = 0 x₃(y₁ − y₂) = 7 × (−4) = −28 Sum = 4 + 0 − 28 = −24 Area = (1/2) · |−24| = 12 square units.

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