Question

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

Explanation:

To determine if two lines (and thus their segments) are perpendicular, we use the property of slopes. If two non - vertical lines have slopes \(m_1\) and \(m_2\), they are perpendicular if and only if \(m_1\times m_2=- 1\), which means \(m_2 =-\frac{1}{m_1}\) (assuming \(m_1
eq0\)). This shows that the slopes are negative reciprocals of each other.

• Option A: If slopes are just reciprocals (\(m_2=\frac{1}{m_1}\)), their product is \(1\), not \(- 1\), so they are not perpendicular.
• Option C: Equal slopes mean the lines are parallel, not perpendicular.
• Option D: If one slope is the negative of the other (\(m_2=-m_1\)), their product is \(-m_1^2\), which is not equal to \(-1\) in general, so they are not perpendicular.

Answer:

B. Their slopes are negative reciprocals.