Question
AB←→is perpendicular to CD←→. If AB←→has a slope of 8/5 what is the slope of CD←→? (1 point) Responses
8/-5
-8/5
8/5
-5/8
8/-5
-8/5
8/5
-5/8
Answers
GPT-4o mini
If two lines are perpendicular, the product of their slopes is -1.
Given that the slope of line \( AB \) is \( \frac{8}{5} \), we can find the slope of line \( CD \) by using the formula:
\[
m_{AB} \cdot m_{CD} = -1
\]
Let \( m_{CD} \) be the slope of line \( CD \):
\[
\frac{8}{5} \cdot m_{CD} = -1
\]
To find \( m_{CD} \), we can solve for \( m_{CD} \):
\[
m_{CD} = -\frac{1}{\frac{8}{5}} = -\frac{5}{8}
\]
Thus, the slope of line \( CD \) is \( -\frac{5}{8} \).
The correct response is:
**-5/8**
Given that the slope of line \( AB \) is \( \frac{8}{5} \), we can find the slope of line \( CD \) by using the formula:
\[
m_{AB} \cdot m_{CD} = -1
\]
Let \( m_{CD} \) be the slope of line \( CD \):
\[
\frac{8}{5} \cdot m_{CD} = -1
\]
To find \( m_{CD} \), we can solve for \( m_{CD} \):
\[
m_{CD} = -\frac{1}{\frac{8}{5}} = -\frac{5}{8}
\]
Thus, the slope of line \( CD \) is \( -\frac{5}{8} \).
The correct response is:
**-5/8**