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Question
Answer the following question:
Find the area of triangle whose vertices are P(3, 6), Q(−1, 3), R(2, −1)
Solution
Here, P(x1, y1) ≡ P(3, 6), Q(x2, y2) ≡ Q(–1, 3), R(x3, y3), ≡ R(2, – 1)
Area of a triangle = `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|`
∴ A(ΔPQR) = `1/2|(3, 6, 1),(-1, 3, 1),(2, -1, 1)|`
= `1/2[3(3 + 1) - 6(-1 - 2) + 1(1 - 6)]`
= `1/2[3(4) - 6(-3) + 1(-5)]`
= `1/2(12 + 18 - 5)`
∴ A(ΔPQR) = `25/2"sq. units"`
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