IDNLearn.com provides a reliable platform for finding accurate and timely answers. Join our knowledgeable community to find the answers you need for any topic or issue.
Sagot :
To determine the slope of a line perpendicular to line [tex]\( m \)[/tex], we start with some fundamental concepts about slopes of perpendicular lines.
Given:
- Line [tex]\( m \)[/tex] has a slope of [tex]\(\frac{p}{q}\)[/tex].
To find:
- The slope of a line perpendicular to line [tex]\( m \)[/tex].
### Step-by-Step Solution:
1. Identify the slope of the given line:
The slope of line [tex]\( m \)[/tex] is [tex]\(\frac{p}{q}\)[/tex].
2. Understand the properties of perpendicular lines:
Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This is known as the negative reciprocal relationship. If [tex]\( m_1 \)[/tex] is the slope of the first line and [tex]\( m_2 \)[/tex] is the slope of the line perpendicular to it, then:
[tex]\[ m_1 \times m_2 = -1 \][/tex]
3. Calculate the slope of the perpendicular line:
Let's denote the slope of the line perpendicular to line [tex]\( m \)[/tex] as [tex]\( m_{\perp} \)[/tex].
According to the property of perpendicular slopes:
[tex]\[ \frac{p}{q} \times m_{\perp} = -1 \][/tex]
To find [tex]\( m_{\perp} \)[/tex], solve for [tex]\( m_{\perp} \)[/tex]:
[tex]\[ m_{\perp} = -\frac{1}{\frac{p}{q}} \][/tex]
4. Simplify the expression:
Simplifying the fraction:
[tex]\[ m_{\perp} = -\frac{q}{p} \][/tex]
### Conclusion:
The slope of the line perpendicular to line [tex]\( m \)[/tex], which has a slope of [tex]\(\frac{p}{q}\)[/tex], is:
[tex]\[ -\frac{q}{p} \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{-\frac{q}{p}} \][/tex]
So, the correct answer is option B.
Given:
- Line [tex]\( m \)[/tex] has a slope of [tex]\(\frac{p}{q}\)[/tex].
To find:
- The slope of a line perpendicular to line [tex]\( m \)[/tex].
### Step-by-Step Solution:
1. Identify the slope of the given line:
The slope of line [tex]\( m \)[/tex] is [tex]\(\frac{p}{q}\)[/tex].
2. Understand the properties of perpendicular lines:
Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This is known as the negative reciprocal relationship. If [tex]\( m_1 \)[/tex] is the slope of the first line and [tex]\( m_2 \)[/tex] is the slope of the line perpendicular to it, then:
[tex]\[ m_1 \times m_2 = -1 \][/tex]
3. Calculate the slope of the perpendicular line:
Let's denote the slope of the line perpendicular to line [tex]\( m \)[/tex] as [tex]\( m_{\perp} \)[/tex].
According to the property of perpendicular slopes:
[tex]\[ \frac{p}{q} \times m_{\perp} = -1 \][/tex]
To find [tex]\( m_{\perp} \)[/tex], solve for [tex]\( m_{\perp} \)[/tex]:
[tex]\[ m_{\perp} = -\frac{1}{\frac{p}{q}} \][/tex]
4. Simplify the expression:
Simplifying the fraction:
[tex]\[ m_{\perp} = -\frac{q}{p} \][/tex]
### Conclusion:
The slope of the line perpendicular to line [tex]\( m \)[/tex], which has a slope of [tex]\(\frac{p}{q}\)[/tex], is:
[tex]\[ -\frac{q}{p} \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{-\frac{q}{p}} \][/tex]
So, the correct answer is option B.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.