A line passes through the points (1,2) and (5,10). A second line passes through the points (0,6) and (4,4). What is the relationship…

Compute each slope. The first line: $\frac{10 - 2}{5 - 1} = \frac{8}{4} = 2$. The second line: $\frac{4 - 6}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}$. The product of the slopes is $2 \times \left(-\frac{1}{2}\right) = -1$, which means the lines are perpendicular, choice D. Choice A would need equal slopes. Choice B would need equal slopes and a common point. Choice C is false, because lines that are not parallel always intersect somewhere in the plane. Negative reciprocal slopes are the signature of perpendicular lines.