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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 find the negative reciprocal of the given slope.
### Steps to find the perpendicular slope:
1. Understand Negative Reciprocal: The negative reciprocal of a slope [tex]\(m\)[/tex] is [tex]\(-\frac{1}{m}\)[/tex].
2. Calculate the Negative Reciprocal:
Given slope = [tex]\(-\frac{5}{6}\)[/tex],
Negative reciprocal = [tex]\(-\frac{1}{-\frac{5}{6}}\)[/tex]
Simplifying that, we get:
[tex]\[ = \frac{6}{5} \][/tex]
So, a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
### Conclusion:
To determine which among the options (line NO, line PQ, line JK, line LM) is perpendicular, you will need to check which line has a slope of [tex]\(\frac{6}{5}\)[/tex]. However, since you provided no specific information about the slopes of these lines, you would typically need additional details about them to determine the correct answer in a practical situation.
### Steps to find the perpendicular slope:
1. Understand Negative Reciprocal: The negative reciprocal of a slope [tex]\(m\)[/tex] is [tex]\(-\frac{1}{m}\)[/tex].
2. Calculate the Negative Reciprocal:
Given slope = [tex]\(-\frac{5}{6}\)[/tex],
Negative reciprocal = [tex]\(-\frac{1}{-\frac{5}{6}}\)[/tex]
Simplifying that, we get:
[tex]\[ = \frac{6}{5} \][/tex]
So, a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
### Conclusion:
To determine which among the options (line NO, line PQ, line JK, line LM) is perpendicular, you will need to check which line has a slope of [tex]\(\frac{6}{5}\)[/tex]. However, since you provided no specific information about the slopes of these lines, you would typically need additional details about them to determine the correct answer in a practical situation.
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