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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 find the slope of the perpendicular line.
The key concept here is that perpendicular lines have slopes that are negative reciprocals of each other. This means if a line has a slope of [tex]\(m\)[/tex], a line that is perpendicular to it will have a slope of [tex]\(-\frac{1}{m}\)[/tex].
Steps to find the slope of the perpendicular line:
1. Start with the slope of the given line, which is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the reciprocal of this slope: The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
3. Take the negative of the reciprocal to get the slope of the perpendicular line: Since we need the negative reciprocal, change the sign of [tex]\(-\frac{6}{5}\)[/tex] to get [tex]\(\frac{6}{5}\)[/tex].
Thus, a line that has a slope of [tex]\(\frac{6}{5}\)[/tex] would be perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
Now, you need to check each of the lines (line JK, line LM, line NO, line PQ) to see which one has this perpendicular slope [tex]\(\frac{6}{5}\)[/tex]. The line with this slope is the one that is perpendicular to the original line.
The key concept here is that perpendicular lines have slopes that are negative reciprocals of each other. This means if a line has a slope of [tex]\(m\)[/tex], a line that is perpendicular to it will have a slope of [tex]\(-\frac{1}{m}\)[/tex].
Steps to find the slope of the perpendicular line:
1. Start with the slope of the given line, which is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the reciprocal of this slope: The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
3. Take the negative of the reciprocal to get the slope of the perpendicular line: Since we need the negative reciprocal, change the sign of [tex]\(-\frac{6}{5}\)[/tex] to get [tex]\(\frac{6}{5}\)[/tex].
Thus, a line that has a slope of [tex]\(\frac{6}{5}\)[/tex] would be perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
Now, you need to check each of the lines (line JK, line LM, line NO, line PQ) to see which one has this perpendicular slope [tex]\(\frac{6}{5}\)[/tex]. The line with this slope is the one that is perpendicular to the original line.
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