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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 negative reciprocal of the given slope.
Here's how you can find the perpendicular slope:
1. Understand the Concept of Perpendicular Slopes:
- When two lines are perpendicular to each other, the slope of one line is the negative reciprocal of the slope of the other line. This means if the slope of one line is [tex]\(m\)[/tex], the slope of the line perpendicular to it is [tex]\(-\frac{1}{m}\)[/tex].
2. Calculate the Negative Reciprocal:
- Given the original slope is [tex]\(-\frac{5}{6}\)[/tex], we find the negative reciprocal by flipping the fraction and changing the sign.
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Changing the sign gives [tex]\(\frac{6}{5}\)[/tex].
3. Interpreting the Result:
- The slope of any line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] should be [tex]\(\frac{6}{5}\)[/tex].
To identify the specific line from options like line JK, line LM, line NO, and line PQ, you would need additional information about these lines, such as their slopes. If any of these lines has a slope of [tex]\(\frac{6}{5}\)[/tex], it would be perpendicular to the line with the original slope of [tex]\(-\frac{5}{6}\)[/tex].
Here's how you can find the perpendicular slope:
1. Understand the Concept of Perpendicular Slopes:
- When two lines are perpendicular to each other, the slope of one line is the negative reciprocal of the slope of the other line. This means if the slope of one line is [tex]\(m\)[/tex], the slope of the line perpendicular to it is [tex]\(-\frac{1}{m}\)[/tex].
2. Calculate the Negative Reciprocal:
- Given the original slope is [tex]\(-\frac{5}{6}\)[/tex], we find the negative reciprocal by flipping the fraction and changing the sign.
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Changing the sign gives [tex]\(\frac{6}{5}\)[/tex].
3. Interpreting the Result:
- The slope of any line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] should be [tex]\(\frac{6}{5}\)[/tex].
To identify the specific line from options like line JK, line LM, line NO, and line PQ, you would need additional information about these lines, such as their slopes. If any of these lines has a slope of [tex]\(\frac{6}{5}\)[/tex], it would be perpendicular to the line with the original slope of [tex]\(-\frac{5}{6}\)[/tex].
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