What is the area of the triangle with vertices $(-1, -2), (2, 3), (4, -1)$?

Explanation

1. 01

   Area $= \frac{1}{2}\left|\begin{vmatrix}-1 & -2 & 1 \\ 2 & 3 & 1 \\ 4 & -1 & 1\end{vmatrix}\right|$.

2. 02

   The determinant is $-22$, so the area is $11$ square units.