What is the area of the triangle with vertices $(-2, 1), (3, 4), (5, -1)$?

Explanation

1. 01

   Area $= \frac{1}{2}\left|\begin{vmatrix}-2 & 1 & 1 \\ 3 & 4 & 1 \\ 5 & -1 & 1\end{vmatrix}\right|$.

2. 02

   The determinant is $-31$, so the area is $\frac{1}{2} \times 31 = \frac{31}{2}$ square units.