Question

question 1 of 10 how do you know if two line segments are perpendicular? a. their slopes are reciprocals. b. their slopes are equal. c. their slopes are negative reciprocals. d. the slope of one is the negative of the slope of the other.

Explanation:

Step1: Recall slope - perpendicularity relation

In coordinate geometry, if two non - vertical lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$. This means $m_1 =-\frac{1}{m_2}$, so the slope of one is the negative reciprocal of the other.

Step2: Analyze options

• Option A: Just saying slopes are perpendicular is not a clear mathematical description.
• Option B: Slopes being reciprocals ($m_1=\frac{1}{m_2}$) is not correct for perpendicular lines.
• Option C: Equal slopes mean the lines are parallel, not perpendicular.
• Option D: Correctly states the relationship for perpendicular line slopes.

Answer:

D. The slope of one is the negative reciprocal of the slope of the other.