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Answer :
Sure! Let's find out which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
1. Understanding Perpendicular Slopes:
If two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line.
2. Calculate the Negative Reciprocal:
- Start with the original slope, which is [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal involves flipping the fraction and changing the sign. The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex], and changing the sign gives us [tex]\(\frac{6}{5}\)[/tex].
3. Identify the Perpendicular Slope:
- A line that is perpendicular to the given line will have a slope of [tex]\(\frac{6}{5}\)[/tex].
4. Line Selection:
- Without specific information on the slopes of lines JK, LM, NO, and PQ, we cannot determine which line is perpendicular just based on this information. We would need the slopes of those lines to find out which one matches [tex]\(\frac{6}{5}\)[/tex].
In summary, any line with a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
1. Understanding Perpendicular Slopes:
If two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line.
2. Calculate the Negative Reciprocal:
- Start with the original slope, which is [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal involves flipping the fraction and changing the sign. The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex], and changing the sign gives us [tex]\(\frac{6}{5}\)[/tex].
3. Identify the Perpendicular Slope:
- A line that is perpendicular to the given line will have a slope of [tex]\(\frac{6}{5}\)[/tex].
4. Line Selection:
- Without specific information on the slopes of lines JK, LM, NO, and PQ, we cannot determine which line is perpendicular just based on this information. We would need the slopes of those lines to find out which one matches [tex]\(\frac{6}{5}\)[/tex].
In summary, any line with a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
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