Area of a triangle with corners ($x_{1}$, $y_{1}$), ($x_{2}$, $y_{2}$), and ($x_{3}$, $y_{3}$): $A = \frac{1}{2} \det \begin{bmatrix}x_{1} & x_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1\end{bmatrix}$