Question
AB←→
is perpendicular to CD←→
. If AB←→
has a slope of 47
what is the slope of CD←→
? (1 point)
Responses
−47
negative 4 over 7
4−7
4 over negative 7
74
7 fourths
−74
is perpendicular to CD←→
. If AB←→
has a slope of 47
what is the slope of CD←→
? (1 point)
Responses
−47
negative 4 over 7
4−7
4 over negative 7
74
7 fourths
−74
Answers
GPT-4o mini
If two lines are perpendicular, the product of their slopes is -1.
Given that the slope of line \( AB \) is \( 47 \), we can find the slope of line \( CD \) (let's denote it as \( m_{CD} \)) using the relationship:
\[
m_{AB} \cdot m_{CD} = -1
\]
Substituting the known slope:
\[
47 \cdot m_{CD} = -1
\]
To find \( m_{CD} \), we solve for it:
\[
m_{CD} = \frac{-1}{47}
\]
Therefore, the slope of line \( CD \) is \( -\frac{1}{47} \).
From the provided options, it seems none of the choices correspond to \(-\frac{1}{47}\). However, considering the negative reciprocal of the slope of AB being \( -47 \), while this directly does not match up with \( [-\frac{1}{47}, -47] \).
The appropriate interpretation of \( CD \) being perpendicular yielding should lead to the correct negative slope output. Ensure to check if the equivalent representations among the choices reflect that when revisiting slope formats like adjacency signs.
If you meant that the slope relation was directly to output the best match reflective of sign opposition, however, strictly \( m_{CD} = -\frac{1}{47} \) evaluation doesn't match.
After reviewing more thoroughly though, in pure perpendicular terms, you can conclude effectively regardless of sign gearing more towards negative alone framing it as descent.
Given that the slope of line \( AB \) is \( 47 \), we can find the slope of line \( CD \) (let's denote it as \( m_{CD} \)) using the relationship:
\[
m_{AB} \cdot m_{CD} = -1
\]
Substituting the known slope:
\[
47 \cdot m_{CD} = -1
\]
To find \( m_{CD} \), we solve for it:
\[
m_{CD} = \frac{-1}{47}
\]
Therefore, the slope of line \( CD \) is \( -\frac{1}{47} \).
From the provided options, it seems none of the choices correspond to \(-\frac{1}{47}\). However, considering the negative reciprocal of the slope of AB being \( -47 \), while this directly does not match up with \( [-\frac{1}{47}, -47] \).
The appropriate interpretation of \( CD \) being perpendicular yielding should lead to the correct negative slope output. Ensure to check if the equivalent representations among the choices reflect that when revisiting slope formats like adjacency signs.
If you meant that the slope relation was directly to output the best match reflective of sign opposition, however, strictly \( m_{CD} = -\frac{1}{47} \) evaluation doesn't match.
After reviewing more thoroughly though, in pure perpendicular terms, you can conclude effectively regardless of sign gearing more towards negative alone framing it as descent.