Question

Find the area of triangles whose vertices are L(1, 1), M(−2, 2), N(5, 4)

Answer 1

Here, L(x₁, y₁) ≡ L(1, 1), M(x₂, y₂) ≡ M(–2, 2), N(x₃, y₃) ≡ N(5, 4)

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

∴ A(ΔLMN) = `1/2|(1, 1, 1),(-2, 2, 1),(5, 4, 1)|`

= `1/2[1(2 - 4) - 1 (-2 - 5) + 1 (- 8 - 10)]`

= `1/2[1(-2) - 1( - 7) + 1 (- 18)]`

= `1/2(-2 + 7 - 18)`

= `-13/2`

Since, area cannot be negative.

∴ A(ΔLMN) = `13/2` sq. units