Question

Find the area of triangles whose vertices are A(−1, 2), B(2, 4), C(0, 0).

Answer 1

Here, A(x₁, y₁) ≡ A(–1, 2), B(x₂, y₂) ≡ B(2, 4), C(x₃, y₃) ≡ C(0, 0)

Area of a triangle = `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|`

∴ A(ΔABC) = `1/2|(-1, 2, 1),(2, 4, 1),(0, 0, 1)|`

= `1/2[-1(4 - 0) - 2(2 - 0) + 1(0 - 0)]`

= `1/2(-4 - 4)`

= `1/2(- 8)`

= –4

Since the area cannot be negative.

∴ A(ΔABC) = 4 sq. units