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Question
Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3)
Solution
The given points are (0, 0), (1, 2) and (4, 3)
Area of the triangle with vertices
(x1, y1), (x2, y2) and (x3, y3) is
Δ = `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|`
∴ The area of the triangle with vertices (0, 0), (1, 2) and (4, 3) is
Δ = `1/2|(0, 0, 1),(1, 2, 1),(4, 3, 1)|`
Δ = `1/2[1(3 - 8)]`
= `1/2 xx -5`
= `(-5)/2`
Area cannot be negative.
Taking positive value, we have required area Δ = `5/2` sq.units
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