Question
What is the area of triangle ABC with vertices A(1, 2),
B(5, 6), and C(7, 2)?Solution
ATQ, Use the coordinate area formula: Area = (1/2) Β· |xβ(yβ β yβ) + xβ(yβ β yβ) + xβ(yβ β yβ)|. Let A(1,2) β (xβ,yβ), B(5,6) β (xβ,yβ), C(7,2) β (xβ,yβ). Compute: yβ β yβ = 6 β 2 = 4 yβ β yβ = 2 β 2 = 0 yβ β yβ = 2 β 6 = β4 xβ(yβ β yβ) = 1 Γ 4 = 4 xβ(yβ β yβ) = 5 Γ 0 = 0 xβ(yβ β yβ) = 7 Γ (β4) = β28 Sum = 4 + 0 β 28 = β24 Area = (1/2) Β· |β24| = 12 square units.
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