If two lines are perpendicular, their slopes are which of the following?

• A. Negative reciprocal slopes
• B. Positive reciprocal slopes
• C. Equal slopes
• D. Slope undefined

Answer: (A)

When two lines are perpendicular, their slopes are negatives of each other’s reciprocals. If one line has slope m, the line perpendicular to it has slope m_perp such that m × m_perp = -1 (as long as neither line is vertical). This makes the slopes negatives of reciprocals: m_perp = -1/m.

Think through examples: if one line has slope 2, the perpendicular line has slope -1/2; if one has slope -3, the perpendicular slope is 1/3. This relationship comes from the fact that angle measures relate to slopes via tan(θ), and adding 90° to the angle flips the tangent to -cot(θ) = -1/tan(θ).

Edge cases: a horizontal line (slope 0) is perpendicular to a vertical line (undefined slope), which also fits the idea that perpendicular slopes are inverses with a sign change in the non-vertical/non-horizontal case.