If two non-vertical lines are perpendicular, what is the product of their slopes?

• A. 0
• B. 1
• C. 2
• D. -1

Answer: (D)

The key idea is that for two non-vertical lines to be perpendicular, their slopes are negative reciprocals of each other. If one line has slope m, the line perpendicular to it has slope -1/m. Multiplying these together gives m × (-1/m) = -1. That’s why the product is -1.

This relies on both slopes existing (non-vertical lines). If one line were vertical, its slope is undefined, and the product wouldn’t be defined, so the condition doesn’t apply.

A quick check: if one line has slope 2, the perpendicular line has slope -1/2, and their product is -1, confirming the relationship.