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Answer :
To determine which line is perpendicular to a line that has a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to understand the concept of perpendicular slopes.
1. Concept of Perpendicular Slopes: When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. This means that if you have the slope of one line, the slope of the perpendicular line will be the negative reciprocal of the original slope.
2. Finding the Negative Reciprocal:
- Start with the given slope: [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, first reverse the fraction. This gives you [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to get the perpendicular slope: [tex]\(\frac{6}{5}\)[/tex].
Therefore, the slope of the line that is perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
The question is asking us which line is perpendicular to the line having that slope. Unfortunately, without additional information about lines JK, LM, NO, or PQ, such as their equations or slopes, I cannot determine which specific line from the list is perpendicular based solely on this information. Please check if there’s more information given about these lines, such as their equations or slopes.
1. Concept of Perpendicular Slopes: When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. This means that if you have the slope of one line, the slope of the perpendicular line will be the negative reciprocal of the original slope.
2. Finding the Negative Reciprocal:
- Start with the given slope: [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, first reverse the fraction. This gives you [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to get the perpendicular slope: [tex]\(\frac{6}{5}\)[/tex].
Therefore, the slope of the line that is perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
The question is asking us which line is perpendicular to the line having that slope. Unfortunately, without additional information about lines JK, LM, NO, or PQ, such as their equations or slopes, I cannot determine which specific line from the list is perpendicular based solely on this information. Please check if there’s more information given about these lines, such as their equations or slopes.
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