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Question
Find the area of the triangle whose vertices are: (4, 5), (0, 7), (–1, 1)
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Solution
Here, A(x1, y1) ≡ A(4, 5), B(x2, y2) ≡ B(0, 7), C(x3, y3) ≡ C(–1, 1)
Area of a triangle = `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|`
∴ A(Δ ABC) = `1/2|(4, 5, 1),(0, 7, 1),(-1, 1, 1)|`
= `1/2[4(7 - 1) - 5(0 + 1) + 1(0 + 7)]`
∴ A(Δ ABC) = `1/2(24 - 5 + 7)`
= 13 sq.units.
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