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Answer :
To solve the problem, we need to find the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
1. Understand Perpendicular Slopes:
- For two lines to be perpendicular, the product of their slopes must be [tex]\(-1\)[/tex].
- If one line has a slope [tex]\(m\)[/tex], the perpendicular line will have a slope of [tex]\(-\frac{1}{m}\)[/tex], known as the negative reciprocal.
2. Calculate the Negative Reciprocal:
- Given the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
- Find the negative reciprocal:
[tex]\[\text{Perpendicular slope} = -\frac{1}{-\frac{5}{6}} = \frac{6}{5}\][/tex]
3. Conclusion:
- A line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
Since the problem doesn't provide specific numeric slopes for lines JK, LM, NO, or PQ, we cannot directly determine which specific line matches the slope [tex]\(\frac{6}{5}\)[/tex] without additional information. However, the slope for the perpendicular line required is [tex]\(\frac{6}{5}\)[/tex] or equivalently as a decimal, [tex]\(1.2\)[/tex].
1. Understand Perpendicular Slopes:
- For two lines to be perpendicular, the product of their slopes must be [tex]\(-1\)[/tex].
- If one line has a slope [tex]\(m\)[/tex], the perpendicular line will have a slope of [tex]\(-\frac{1}{m}\)[/tex], known as the negative reciprocal.
2. Calculate the Negative Reciprocal:
- Given the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
- Find the negative reciprocal:
[tex]\[\text{Perpendicular slope} = -\frac{1}{-\frac{5}{6}} = \frac{6}{5}\][/tex]
3. Conclusion:
- A line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
Since the problem doesn't provide specific numeric slopes for lines JK, LM, NO, or PQ, we cannot directly determine which specific line matches the slope [tex]\(\frac{6}{5}\)[/tex] without additional information. However, the slope for the perpendicular line required is [tex]\(\frac{6}{5}\)[/tex] or equivalently as a decimal, [tex]\(1.2\)[/tex].
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