Question

question 10 of 10 how do you know if two line segments are perpendicular? a. their slopes are reciprocals. b. the slope of one is the negative of the slope of the other. c. their slopes are negative reciprocals. d. their slopes are equal.

Explanation:

Step1: Recall slope - perpendicularity relation

If two non - vertical lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$, which means $m_1 =-\frac{1}{m_2}$ (negative reciprocals).

Step2: Analyze each option

• Option A: Reciprocals are not enough. For example, slopes 2 and $\frac{1}{2}$ are reciprocals but lines are not perpendicular.
• Option B: Just reciprocals is incorrect as perpendicular lines have negative reciprocals.
• Option C: This is the correct condition for perpendicular lines. If slope of one line is $m$, slope of perpendicular line is $-m$.
• Option D: Equal slopes mean parallel lines, not perpendicular lines.

Answer:

C. The slope of one is the negative of the slope of the other.