Area of Triangle in Determinant Form/Proof 3

Proof

 * Area-of-Triangle-Determinant-Proof-3.png

Let $A$, $B$ and $C$ be defined as $\tuple {x_1, y_1}$, $\tuple {x_2, y_2}$ and $\tuple {x_3, y_3}$ respectively.

From the figure, we see that: