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Answer :
To find which line is perpendicular to a line that has a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine the slope of a line that would meet this criterion.
1. Understanding Perpendicular Slopes:
Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. Therefore, if one line has a slope [tex]\(m\)[/tex], then the slope of the line that is perpendicular would be [tex]\(-\frac{1}{m}\)[/tex].
2. Calculate the Perpendicular Slope:
Given the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], the slope of the perpendicular line would be calculated as follows:
[tex]\[
\text{Perpendicular slope} = -\frac{1}{\left(-\frac{5}{6}\right)}
\][/tex]
Simplifying, this gives:
[tex]\[
\text{Perpendicular slope} = \frac{6}{5}
\][/tex]
Converting [tex]\(\frac{6}{5}\)[/tex] to a decimal, it is [tex]\(1.2\)[/tex].
3. Conclusion:
A line that is perpendicular to one with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(1.2\)[/tex]. You should now check each of the given lines (line JK, line LM, line NO, and line PQ) to see which has a slope of [tex]\(1.2\)[/tex]. That line will be the one perpendicular to the given line.
1. Understanding Perpendicular Slopes:
Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. Therefore, if one line has a slope [tex]\(m\)[/tex], then the slope of the line that is perpendicular would be [tex]\(-\frac{1}{m}\)[/tex].
2. Calculate the Perpendicular Slope:
Given the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], the slope of the perpendicular line would be calculated as follows:
[tex]\[
\text{Perpendicular slope} = -\frac{1}{\left(-\frac{5}{6}\right)}
\][/tex]
Simplifying, this gives:
[tex]\[
\text{Perpendicular slope} = \frac{6}{5}
\][/tex]
Converting [tex]\(\frac{6}{5}\)[/tex] to a decimal, it is [tex]\(1.2\)[/tex].
3. Conclusion:
A line that is perpendicular to one with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(1.2\)[/tex]. You should now check each of the given lines (line JK, line LM, line NO, and line PQ) to see which has a slope of [tex]\(1.2\)[/tex]. That line will be the one perpendicular to the given line.
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