Question

Find the area of triangles whose vertices are P(3, 6), Q(−1, 3), R(2, −1)

Answer 1

Here, P(x₁, y₁) ≡ P(3, 6), Q(x₂, y₂) ≡ Q(−1, 3), R(x₃, y₃) ≡ R(2, −1)

Area of 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