1. **State the problem:** Determine if the line segments AB and CD are parallel, perpendicular, or neither for the points given in problem 18: A(-4, 3), B(2, -12), C(10, 5), and D(0, 1). 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Important rules:** - Two lines are **parallel** if their slopes are equal. - Two lines are **perpendicular** if the product of their slopes is $-1$. 4. **Calculate slope of AB:** $$m_{AB} = \frac{-12 - 3}{2 - (-4)} = \frac{-15}{6} = \frac{\cancel{-15}}{\cancel{6}} = -\frac{5}{2}$$ 5. **Calculate slope of CD:** $$m_{CD} = \frac{1 - 5}{0 - 10} = \frac{-4}{-10} = \frac{\cancel{-4}}{\cancel{-10}} = \frac{2}{5}$$ 6. **Check if parallel:** $$m_{AB} = -\frac{5}{2} \neq m_{CD} = \frac{2}{5}$$ Not parallel. 7. **Check if perpendicular:** $$m_{AB} \times m_{CD} = -\frac{5}{2} \times \frac{2}{5} = -1$$ Since the product is $-1$, the lines AB and CD are perpendicular. **Final answer:** Lines AB and CD are perpendicular.