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Answer :
Sure! To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the perpendicular line.
1. Understanding Perpendicular Slopes: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This means that if you know the slope of one line, the slope of the perpendicular line can be found by taking the negative reciprocal of the original slope.
2. Finding the Negative Reciprocal:
- The slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
- To find the slope of the perpendicular line, take the negative reciprocal. The negative reciprocal of a fraction [tex]\(\frac{a}{b}\)[/tex] is [tex]\(\frac{-b}{a}\)[/tex].
- Therefore, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
3. Result: The slope of the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
So, the line with a slope of [tex]\(\frac{6}{5}\)[/tex] is the one that is perpendicular to the given line. From the list provided, you would need more information about the slopes of line JK, line LM, line NO, and line PQ to identify which one has that slope.
1. Understanding Perpendicular Slopes: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This means that if you know the slope of one line, the slope of the perpendicular line can be found by taking the negative reciprocal of the original slope.
2. Finding the Negative Reciprocal:
- The slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
- To find the slope of the perpendicular line, take the negative reciprocal. The negative reciprocal of a fraction [tex]\(\frac{a}{b}\)[/tex] is [tex]\(\frac{-b}{a}\)[/tex].
- Therefore, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
3. Result: The slope of the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
So, the line with a slope of [tex]\(\frac{6}{5}\)[/tex] is the one that is perpendicular to the given line. From the list provided, you would need more information about the slopes of line JK, line LM, line NO, and line PQ to identify which one has that slope.
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