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Answer :
To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to use the concept of perpendicular slopes.
1. Understand the concept of perpendicular slopes: The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope.
2. Calculate the negative reciprocal: If the original slope is [tex]\(-\frac{5}{6}\)[/tex], to find the perpendicular slope, we take the negative reciprocal:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- The negative reciprocal, therefore, is [tex]\(\frac{6}{5}\)[/tex].
3. Conclusion: A line that is perpendicular to one with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
Without additional information on the slopes of lines JK, LM, NO, and [tex]\(PQ\)[/tex], we cannot definitively specify which of these lines is perpendicular to one with a slope of [tex]\(-\frac{5}{6}\)[/tex]. However, any line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be perpendicular to such a line. Therefore, you would need to know the slopes of the lines listed to identify which one matches this condition.
1. Understand the concept of perpendicular slopes: The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope.
2. Calculate the negative reciprocal: If the original slope is [tex]\(-\frac{5}{6}\)[/tex], to find the perpendicular slope, we take the negative reciprocal:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- The negative reciprocal, therefore, is [tex]\(\frac{6}{5}\)[/tex].
3. Conclusion: A line that is perpendicular to one with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
Without additional information on the slopes of lines JK, LM, NO, and [tex]\(PQ\)[/tex], we cannot definitively specify which of these lines is perpendicular to one with a slope of [tex]\(-\frac{5}{6}\)[/tex]. However, any line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be perpendicular to such a line. Therefore, you would need to know the slopes of the lines listed to identify which one matches this condition.
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