What is the area of the triangle with vertices $(1, 2), (4, 6), (7, 3)$?

Explanation

1. 01

   Area $= \frac{1}{2}\left|\begin{vmatrix}1 & 2 & 1 \\ 4 & 6 & 1 \\ 7 & 3 & 1\end{vmatrix}\right|$.

2. 02

   The determinant is $-21$, so the area is $\frac{1}{2} \times 21 = \frac{21}{2}$ square units.