Area of Triangle in Determinant Form with Vertex at Origin

Example of Area of Triangle in Determinant Form
Let $A = \tuple {0, 0}, B = \tuple {b, a}, C = \tuple {x, y}$ be points in the Cartesian plane.

Let $T$ the triangle whose vertices are at $A$, $B$ and $C$.

Then the area $\mathcal A$ of $T$ is:
 * $\map \Area T = \dfrac {\size {b y - a x} } 2$