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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 find the slope of the perpendicular line.
1. Understanding Perpendicular Slopes:
- If two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
- This means that if one line has a slope of [tex]\(m\)[/tex], the slope of a line perpendicular to it is [tex]\(-\frac{1}{m}\)[/tex].
2. Apply the Concept:
- Given the original slope [tex]\(m = -\frac{5}{6}\)[/tex].
- The slope of the perpendicular line is calculated as:
[tex]\[
\text{Perpendicular Slope} = -\left(\frac{1}{-\frac{5}{6}}\right) = \frac{6}{5}
\][/tex]
3. Simplifying the Result:
- The slope of the perpendicular line is [tex]\(\frac{6}{5}\)[/tex].
Therefore, whichever line (either line JK, LM, NO, or PQ) has a slope of [tex]\(\frac{6}{5}\)[/tex] will be the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. You would need additional information about the specific slopes of lines JK, LM, NO, and PQ to determine the exact line that meets this condition.
1. Understanding Perpendicular Slopes:
- If two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
- This means that if one line has a slope of [tex]\(m\)[/tex], the slope of a line perpendicular to it is [tex]\(-\frac{1}{m}\)[/tex].
2. Apply the Concept:
- Given the original slope [tex]\(m = -\frac{5}{6}\)[/tex].
- The slope of the perpendicular line is calculated as:
[tex]\[
\text{Perpendicular Slope} = -\left(\frac{1}{-\frac{5}{6}}\right) = \frac{6}{5}
\][/tex]
3. Simplifying the Result:
- The slope of the perpendicular line is [tex]\(\frac{6}{5}\)[/tex].
Therefore, whichever line (either line JK, LM, NO, or PQ) has a slope of [tex]\(\frac{6}{5}\)[/tex] will be the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. You would need additional information about the specific slopes of lines JK, LM, NO, and PQ to determine the exact line that meets this condition.
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