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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 understand the concept of perpendicular slopes.
1. Find the Perpendicular Slope:
- The slope of a line that is perpendicular to another is the negative reciprocal of the original line's slope.
- Start with the given slope: [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal means we take the opposite sign and flip the fraction.
- So, the reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
- As a result, the slope of the line perpendicular to the original line is [tex]\(\frac{6}{5}\)[/tex].
2. Determine the Correct Line:
- Check the list of lines (line JK, line LM, line NO, line PQ) to find the one with a slope of [tex]\(\frac{6}{5}\)[/tex].
- Since the question doesn't provide specific information about the slopes of these lines, we generally don't have the answer directly. Usually, you would need additional details, like equations for these lines, to match the slope.
In a practical scenario, you'd identify the line with a slope matching the calculated perpendicular slope of [tex]\(\frac{6}{5}\)[/tex]. If additional information regarding the slopes of lines JK, LM, NO, and PQ were provided, you would pick that line from the options.
1. Find the Perpendicular Slope:
- The slope of a line that is perpendicular to another is the negative reciprocal of the original line's slope.
- Start with the given slope: [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal means we take the opposite sign and flip the fraction.
- So, the reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
- As a result, the slope of the line perpendicular to the original line is [tex]\(\frac{6}{5}\)[/tex].
2. Determine the Correct Line:
- Check the list of lines (line JK, line LM, line NO, line PQ) to find the one with a slope of [tex]\(\frac{6}{5}\)[/tex].
- Since the question doesn't provide specific information about the slopes of these lines, we generally don't have the answer directly. Usually, you would need additional details, like equations for these lines, to match the slope.
In a practical scenario, you'd identify the line with a slope matching the calculated perpendicular slope of [tex]\(\frac{6}{5}\)[/tex]. If additional information regarding the slopes of lines JK, LM, NO, and PQ were provided, you would pick that line from the options.
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