The triangle with vertices $(0, 2), (4, 2), (0, k)$ has area 6 square units. What are the possible values of $k$?

Explanation

1. 01

   The determinant is $4 k - 8$, and $\frac{1}{2}\left|4 k - 8\right| = 6$, so $4 k - 8 = \pm 12$.

2. 02

   The two signs give $k = -1$ and $k = 5$.