Answer :

Given vertices of the triangle are (–2, –3), (3, 2), (–1, –8)

Let the vertices of the triangle be given by (x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

Area of triangle is given by Δ =

Area of triangle = Δ =

Expanding the determinant along Row 1

Δ = 1/2 × |[(-2) × (2 × 1 – (-8) × 1) – (-3) × (3 × 1 – (-1) × 1) + 1 × (3 × (-8) – 2 × (-1))]|

Δ = 1/2 × |[(-2) × (2 + 8) + 3 × (3 + 1) + 1 × (-24 + 2)]|

Δ = 1/2 × |[(-2) × 10 + 3 × 4 + 1 × (-22)]| = 1/2 ×| (-20 + 12 – 22)| sq. units

Δ = 1/2 × |-30| sq. units = 30/2 sq. units

∴ Δ = 30/2 sq. units = 15 sq. units

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