Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof resit / 4 / a / Solution

Subtract the first vertex from the other two, giving side vectors $(2,1)$ and $(3,4)$. Their determinant is $2\cdot 4-3\cdot 1=5$, the signed area of the corresponding parallelogram. The triangle occupies half that area, hence its area is $5/2$. Taking the absolute value would remove any sign change caused by reversing the vertex order. This is the determinant formula for triangle area.