Asked by hihi
Given that lines l 𝑙 and n 𝑛 are perpendicular, which of the following is part of the proof that l 𝑙 and n 𝑛 have slopes that are opposite reciprocals? (1 point) Responses △ABC∼△EDA, ABC≅DAE, The slope of line 𝑙 is BC/CA and the slope of line n 𝑛 is DE/AD, BC/CA=−DE/AD
Answers
Answered by
hihi
theres only one answer girl
Answered by
GPT-4o mini
To show that two lines \( l \) and \( n \) are perpendicular and that their slopes are opposite reciprocals, we can follow the reasoning involving the slopes of those lines.
Given the choices in your question, the relevant part of the proof to demonstrate that the slopes of lines \( l \) and \( n \) are opposite reciprocals would typically include:
- The slopes of lines \( l \) and \( n \) expressed in terms of vertical and horizontal changes.
- The relationship that if line \( l \) has a slope of \( m \), then the slope of line \( n \) (which is perpendicular to \( l \)) will be \( -1/m \), indicating they are opposite reciprocals.
From the options you’ve listed, the statement that includes the slopes and suggests a relationship between them would be the most relevant. So, if the statement in the options is:
"The slope of line \( l \) is \( \frac{BC}{CA} \) and the slope of line \( n \) is \( \frac{DE}{AD} \), and \( \frac{BC}{CA} = -\frac{DE}{AD} \)",
This directly shows the relationship between the slopes of lines \( l \) and \( n \), indicating that the slopes are opposite signs and reciprocals of one another, which is the key condition for two lines to be perpendicular.
Therefore, the correct response is: **"The slope of line \( l \) is \( \frac{BC}{CA} \) and the slope of line \( n \) is \( \frac{DE}{AD} \), \( \frac{BC}{CA} = -\frac{DE}{AD} \)."**
Given the choices in your question, the relevant part of the proof to demonstrate that the slopes of lines \( l \) and \( n \) are opposite reciprocals would typically include:
- The slopes of lines \( l \) and \( n \) expressed in terms of vertical and horizontal changes.
- The relationship that if line \( l \) has a slope of \( m \), then the slope of line \( n \) (which is perpendicular to \( l \)) will be \( -1/m \), indicating they are opposite reciprocals.
From the options you’ve listed, the statement that includes the slopes and suggests a relationship between them would be the most relevant. So, if the statement in the options is:
"The slope of line \( l \) is \( \frac{BC}{CA} \) and the slope of line \( n \) is \( \frac{DE}{AD} \), and \( \frac{BC}{CA} = -\frac{DE}{AD} \)",
This directly shows the relationship between the slopes of lines \( l \) and \( n \), indicating that the slopes are opposite signs and reciprocals of one another, which is the key condition for two lines to be perpendicular.
Therefore, the correct response is: **"The slope of line \( l \) is \( \frac{BC}{CA} \) and the slope of line \( n \) is \( \frac{DE}{AD} \), \( \frac{BC}{CA} = -\frac{DE}{AD} \)."**
Answered by
GPT-4o mini
Apologies for the confusion! Based on the options you provided, the best choice that supports the proof that lines \( l \) and \( n \) are perpendicular by showing their slopes are opposite reciprocals is:
**"The slope of line \( l \) is \( \frac{BC}{CA} \) and the slope of line \( n \) is \( \frac{DE}{AD} \), \( \frac{BC}{CA} = -\frac{DE}{AD}."**
This statement directly addresses the slopes of the two lines and indicates their relationship, which is essential for proving that they are perpendicular.
**"The slope of line \( l \) is \( \frac{BC}{CA} \) and the slope of line \( n \) is \( \frac{DE}{AD} \), \( \frac{BC}{CA} = -\frac{DE}{AD}."**
This statement directly addresses the slopes of the two lines and indicates their relationship, which is essential for proving that they are perpendicular.