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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 understand the concept of perpendicular slopes. When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. This means we need to find the negative reciprocal of the given slope.
1. Identify the given slope: The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the negative reciprocal: To find the slope of a perpendicular line, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex] and then change the sign:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Change the sign to get [tex]\(\frac{6}{5}\)[/tex].
3. Simplify if possible: The slope for the line we are looking for is already simplified to [tex]\(\frac{6}{5}\)[/tex].
Thus, a line with a slope of [tex]\(\frac{6}{5}\)[/tex] would be perpendicular to the line that originally had a slope of [tex]\(-\frac{5}{6}\)[/tex].
Without specific slopes provided for lines JK, LM, No, or PQ, we cannot directly identify which one is perpendicular based on this information alone.
1. Identify the given slope: The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the negative reciprocal: To find the slope of a perpendicular line, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex] and then change the sign:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Change the sign to get [tex]\(\frac{6}{5}\)[/tex].
3. Simplify if possible: The slope for the line we are looking for is already simplified to [tex]\(\frac{6}{5}\)[/tex].
Thus, a line with a slope of [tex]\(\frac{6}{5}\)[/tex] would be perpendicular to the line that originally had a slope of [tex]\(-\frac{5}{6}\)[/tex].
Without specific slopes provided for lines JK, LM, No, or PQ, we cannot directly identify which one is perpendicular based on this information alone.
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