Question

slopes of perpendicular lines the slopes of two lines are given. are the lines perpendicular? 10. ( m _ { 1 } = \frac { 5 } { 7 } ), ( m _ { 2 } = - \frac { 7 } { 5 } )

Explanation:

Step1: Recall the condition for perpendicular lines

Two lines with slopes \(m_1\) and \(m_2\) are perpendicular if \(m_1\times m_2=- 1\).

Step2: Calculate the product of the given slopes

Given \(m_1 = \frac{5}{7}\) and \(m_2=-\frac{7}{5}\), then \(m_1\times m_2=\frac{5}{7}\times(-\frac{7}{5})\).
Using the rule for multiplying fractions \(\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}\), we have \(\frac{5\times(-7)}{7\times5}=\frac{-35}{35}=-1\).

Answer:

Yes, the lines are perpendicular.