Area of Triangle in Determinant Form/Examples/Vertices at (-4-i), (1+2i), (4-3i)

Example of Area of Triangle in Determinant Form
Let $T$ be a triangle embedded in the complex plane with vertices at $\paren {-4 - i}, \paren {1 + 2 i}, \paren {4 - 3 i}$.

The area of $T$ is given by:


 * $\map \Area T = 17$

Proof
From Area of Triangle in Determinant Form:

$\map \Area T = \dfrac 1 2 \size {\paren {\begin{vmatrix} -4 & -1 & 1 \\ 1 & 2 & 1 \\ 4 & -3 & 1 \\ \end{vmatrix} } }$