To determine the slope of a line that is perpendicular to line [tex]\( m \)[/tex], we need to understand the principles of the slope for perpendicular lines.
1. Slope of line [tex]\( m \)[/tex]:
The problem states that the slope of line [tex]\( m \)[/tex] is [tex]\(\frac{R}{q}\)[/tex].
2. Slope of a perpendicular line:
The slope of any line that is perpendicular to another line is the negative reciprocal of the original line's slope.
3. Calculation:
To find the negative reciprocal of [tex]\(\frac{R}{q}\)[/tex]:
- First, find the reciprocal of [tex]\(\frac{R}{q}\)[/tex]. The reciprocal of [tex]\(\frac{R}{q}\)[/tex] is [tex]\(\frac{q}{R}\)[/tex].
- Then, take the negative of the reciprocal. The negative of [tex]\(\frac{q}{R}\)[/tex] is [tex]\(-\frac{q}{R}\)[/tex].
4. Summary:
Thus, the slope of the line that is perpendicular to line [tex]\( m \)[/tex], which has a slope of [tex]\(\frac{R}{q}\)[/tex], is [tex]\(-\frac{q}{R}\)[/tex].
Now, matching this result with the given options:
- Option A. [tex]\( -\frac{q}{p} \)[/tex]
- Option B. [tex]\( \frac{q}{p} \)[/tex]
- Option C. [tex]\( -\frac{p}{q} \)[/tex]
- Option D. [tex]\( \frac{p}{q} \)[/tex]
The correct answer, [tex]\( -\frac{q}{R} \)[/tex], matches none of the given options directly as we have a mismatch in terms of [tex]\( R \)[/tex] vs. [tex]\( p \)[/tex]. However, based on the problem statement, one of the given options should logically substitute [tex]\( R \)[/tex] with the correct variable. Given that [tex]\( p \neq q \)[/tex] and assessing the context, we need to align correctly, implying a slight possible variable outline error or a logical extension.
Correct conclusion:
- Therefore, based on our correct calculation, the slope of the line perpendicular to line m mirroring correct variables in options should indeed be considered close to option [tex]\( C \)[/tex].
So, the best-match answer from the problem context is:
C. [tex]\( -\frac{p}{q} \)[/tex]
