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Answer :
To find a line perpendicular to a line with a given slope, we need to use the concept of perpendicular slopes. Here's a step-by-step explanation:
1. Understand the Slope Given: The slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the Perpendicular Slope: Lines that are perpendicular to each other have slopes that are negative reciprocals. A negative reciprocal is found by flipping the fraction of the slope and changing its sign.
- For the slope [tex]\(-\frac{5}{6}\)[/tex], calculate the negative reciprocal:
- Flip the fraction: [tex]\(\frac{6}{5}\)[/tex]
- Change the sign to positive: [tex]\(\frac{6}{5}\)[/tex]
3. Conclusion: A line that is perpendicular to the line with the slope [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
4. Interpretation: One of the given lines (JK, LM, NO, PQ) will have a slope of [tex]\(\frac{6}{5}\)[/tex]. Identify which line it is to answer the question correctly.
So, when given choices such as line JK, LM, NO, or PQ, the correct answer would be the one with a slope of [tex]\(\frac{6}{5}\)[/tex].
1. Understand the Slope Given: The slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the Perpendicular Slope: Lines that are perpendicular to each other have slopes that are negative reciprocals. A negative reciprocal is found by flipping the fraction of the slope and changing its sign.
- For the slope [tex]\(-\frac{5}{6}\)[/tex], calculate the negative reciprocal:
- Flip the fraction: [tex]\(\frac{6}{5}\)[/tex]
- Change the sign to positive: [tex]\(\frac{6}{5}\)[/tex]
3. Conclusion: A line that is perpendicular to the line with the slope [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
4. Interpretation: One of the given lines (JK, LM, NO, PQ) will have a slope of [tex]\(\frac{6}{5}\)[/tex]. Identify which line it is to answer the question correctly.
So, when given choices such as line JK, LM, NO, or PQ, the correct answer would be the one with a slope of [tex]\(\frac{6}{5}\)[/tex].
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