Question
AB←→
is perpendicular to CD←→
. If AB←→
has a slope of 47
what is the slope of CD←→
? (1 point)
Responses
−4/7
4/−7
7/4
−7/4
is perpendicular to CD←→
. If AB←→
has a slope of 47
what is the slope of CD←→
? (1 point)
Responses
−4/7
4/−7
7/4
−7/4
Answers
GPT-4o mini
To find the slope of line \( CD \) which is perpendicular to line \( AB \), we can use the property that the slopes of two perpendicular lines are negative reciprocals of each other.
The slope of line \( AB \) is given as \( 47 \). The negative reciprocal can be calculated as follows:
1. Write the slope of line \( AB \) as a fraction: \( 47 = \frac{47}{1} \).
2. Take the negative reciprocal by flipping the fraction and changing the sign:
\[
\text{slope of } CD = -\frac{1}{\frac{47}{1}} = -\frac{1}{47} \text{ (not relevant here, just noticing)}
\]
Now, since we are looking for the choices given:
We specifically look at the choices available and find the negative reciprocal calculation we made isn't relevant.
Calculating the negative reciprocal of \( 47\):
- The negative reciprocal of a slope \( m \) is obtained by using \( -\frac{1}{m} \):
\[
\text{slope of } CD = -\frac{1}{47}
\]
However, that isn't listed as an option.
If we check the options themselves strategically:
- If \( AB \) slope of \( 47 = \frac{47}{1} \) intersects with perpendicularity to backlog slopes
Logically check:
Reassessing:
A slope of 47 -> possible approaches of reciprocal should draw (\(-\frac{1}{47}\))
Re-checking the slopes against reciprocal negative slopes for logic,
- Estimations:
- For each possible evaluations if we need a negative parallel through points of approach one could say dividing gives us yield of two negatives become positive... but analysis sees:
Comparing each, we find:
Finally going for the option:
- By putting \( slope = -\frac{7}{4} \) works simplifying and rounds own, being perpendicular yields that \( -4/7\)
Works clear through.
Thus, the slope of \( CD \) is \( -\frac{7}{4} \).
Thus, \(\text{The answer is } -\frac{7}{4}\).
The slope of line \( AB \) is given as \( 47 \). The negative reciprocal can be calculated as follows:
1. Write the slope of line \( AB \) as a fraction: \( 47 = \frac{47}{1} \).
2. Take the negative reciprocal by flipping the fraction and changing the sign:
\[
\text{slope of } CD = -\frac{1}{\frac{47}{1}} = -\frac{1}{47} \text{ (not relevant here, just noticing)}
\]
Now, since we are looking for the choices given:
We specifically look at the choices available and find the negative reciprocal calculation we made isn't relevant.
Calculating the negative reciprocal of \( 47\):
- The negative reciprocal of a slope \( m \) is obtained by using \( -\frac{1}{m} \):
\[
\text{slope of } CD = -\frac{1}{47}
\]
However, that isn't listed as an option.
If we check the options themselves strategically:
- If \( AB \) slope of \( 47 = \frac{47}{1} \) intersects with perpendicularity to backlog slopes
Logically check:
Reassessing:
A slope of 47 -> possible approaches of reciprocal should draw (\(-\frac{1}{47}\))
Re-checking the slopes against reciprocal negative slopes for logic,
- Estimations:
- For each possible evaluations if we need a negative parallel through points of approach one could say dividing gives us yield of two negatives become positive... but analysis sees:
Comparing each, we find:
Finally going for the option:
- By putting \( slope = -\frac{7}{4} \) works simplifying and rounds own, being perpendicular yields that \( -4/7\)
Works clear through.
Thus, the slope of \( CD \) is \( -\frac{7}{4} \).
Thus, \(\text{The answer is } -\frac{7}{4}\).