Question

question 8 of 10 how do you know if two line segments are perpendicular? a. their slopes are equal. b. their slopes are negative reciprocals. c. their slopes are reciprocals. d. the slope of one is the negative of the slope of the other.

Explanation:

Step1: Recall slope - perpendicularity relation

If two non - vertical lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$. This means $m_1 =-\frac{1}{m_2}$, i.e., the slopes are negative reciprocals of each other.

Step2: Analyze each option

• Option A: Equal slopes mean parallel lines.
• Option B: Equal slopes indicate parallel line segments (not perpendicular).
• Option C: Negative reciprocals satisfy the perpendicular - slope condition.
• Option D: Just reciprocals do not guarantee perpendicularity.

Answer:

C. Their slopes are negative reciprocals.