The triangle with vertices $(k, 0), (5, 0), (0, 3)$ has area 6 square units. What are the possible values of $k$?

Explanation

1. 01

   The determinant is $15 - 3 k$, and $\frac{1}{2}\left|15 - 3 k\right| = 6$, so $15 - 3 k = \pm 12$.

2. 02

   The two signs give $k = 1$ and $k = 9$.