Question

Find the area of the triangle whose vertices are: (4, 5), (0, 7), (–1, 1)

Answer 1

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.