Find area of the triangle with vertices at the point given in each of the following:

(2, 7), (1, 1), (10, 8)

Given vertices of the triangle are (2, 7), (1, 1), (10, 8)

Let the vertices of the triangle be given by (x₁, y₁), (x₂, y₂), (x₃, y₃)

Area of triangle is given by Δ =

Area of triangle = Δ =

Expanding the determinant along Row 1

Δ = 1/2 × [2 × (1 × 1 – 8 × 1) – 7 × (1 × 1 – 10 × 1) + 1 × (8 × 1 – 1 × 10)]

Δ = 1/2 × [2 × (1 – 8) – 7 × (1 – 10) + 1 × (8 – 10)]

Δ = 1/2 × [2 × (-7) – 7 × (-9) + 1 × (-2)] = 1/2 × (-14 + 63 – 2) sq. units

Δ = 1/2 × 47 sq. units = 47/2 sq. units

∴ Δ = 47/2 sq. units = 23.5 sq. units