Area of Triangle in Determinant Form

Theorem
Let $A = \tuple {x_1, y_1}, B = \tuple {x_2, y_2}, C = \tuple {x_3, y_3}$ be points in the Cartesian plane.

The area $\AA$ of the triangle whose vertices are at $A$, $B$ and $C$ is given by:


 * $\AA = \dfrac 1 2 \size {\paren {\begin {vmatrix}

x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \\ \end {vmatrix} } }$