If the lines are parallel, they have the same slope. If lines are perpendicular, they have the negative reciprocal slope. We can use the points to find the slopes of each segment, then evaluate if they are parallel, perpendicular, or neither.
The formula for slope is [tex] \frac{y_2-y_1}{x_2-x_1} [/tex]
Line BC: In this case, we have the points (4,-5) and (3,2). x₁=4, y₁=-5, x₂=3, y₂=2. We plug those numbers in, and the slope is -7
Line DE: In this case, we have the points (2,0) and (9,1), where x₁=2, y₁=0, x₂=9, y₂=1. We plug those numbers in, and the slope is 1/7
Therefore, the lines are B. Perpendicular because the difference between the slopes is that it is the negative (lost the negative sign) and the reciprocal (7 became 1/7)
