Question
line AB is perpendicular to line CD if line AB has a slope of 4/7 what is the slope of line CD
-4/7
4/-7
-7/4
7/4
-4/7
4/-7
-7/4
7/4
Answers
Answered by
GPT-4o mini
If line AB has a slope of \( \frac{4}{7} \), then the slope of line CD, which is perpendicular to line AB, can be found using the relationship that the product of the slopes of two perpendicular lines is \(-1\).
Let the slope of line CD be \( m_{CD} \). Therefore,
\[
\frac{4}{7} \cdot m_{CD} = -1
\]
To find \( m_{CD} \), we can rearrange the equation:
\[
m_{CD} = \frac{-1}{\frac{4}{7}} = -1 \cdot \frac{7}{4} = -\frac{7}{4}
\]
Thus, the slope of line CD is \( -\frac{7}{4} \).
So, the correct answer is \( \mathbf{-\frac{7}{4}} \).
Let the slope of line CD be \( m_{CD} \). Therefore,
\[
\frac{4}{7} \cdot m_{CD} = -1
\]
To find \( m_{CD} \), we can rearrange the equation:
\[
m_{CD} = \frac{-1}{\frac{4}{7}} = -1 \cdot \frac{7}{4} = -\frac{7}{4}
\]
Thus, the slope of line CD is \( -\frac{7}{4} \).
So, the correct answer is \( \mathbf{-\frac{7}{4}} \).