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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 line that would be perpendicular to it.
Here's a step-by-step explanation:
1. Understand Perpendicular Slopes: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This means that the slope of a perpendicular line is the negative reciprocal of the original line's slope.
2. Find the Negative Reciprocal: The original slope given is [tex]\(-\frac{5}{6}\)[/tex]. To find the negative reciprocal, you flip the fraction and change the sign.
- Flip the fraction: Change [tex]\(-\frac{5}{6}\)[/tex] to [tex]\(\frac{6}{5}\)[/tex].
- Change the sign: Since the original slope is negative, the perpendicular slope will be positive. So, the perpendicular slope becomes [tex]\(\frac{6}{5}\)[/tex].
3. Check the Slope: The perpendicular slope calculated is [tex]\(\frac{6}{5}\)[/tex], which is equivalent to 1.2 when expressed as a decimal.
4. Match with Given Lines: Since none of the lines (JK, LM, NO, PQ) has a specifically given slope in the problem, you would need additional information (like coordinates or angles) to determine which of these lines actually has a slope of 1.2.
Since the specific slopes for these lines are not provided in the question, the final step would involve obtaining more details on these lines to find out which one matches [tex]\(\frac{6}{5}\)[/tex]. If any additional details are available, please let me know, and I can assist you further.
Here's a step-by-step explanation:
1. Understand Perpendicular Slopes: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This means that the slope of a perpendicular line is the negative reciprocal of the original line's slope.
2. Find the Negative Reciprocal: The original slope given is [tex]\(-\frac{5}{6}\)[/tex]. To find the negative reciprocal, you flip the fraction and change the sign.
- Flip the fraction: Change [tex]\(-\frac{5}{6}\)[/tex] to [tex]\(\frac{6}{5}\)[/tex].
- Change the sign: Since the original slope is negative, the perpendicular slope will be positive. So, the perpendicular slope becomes [tex]\(\frac{6}{5}\)[/tex].
3. Check the Slope: The perpendicular slope calculated is [tex]\(\frac{6}{5}\)[/tex], which is equivalent to 1.2 when expressed as a decimal.
4. Match with Given Lines: Since none of the lines (JK, LM, NO, PQ) has a specifically given slope in the problem, you would need additional information (like coordinates or angles) to determine which of these lines actually has a slope of 1.2.
Since the specific slopes for these lines are not provided in the question, the final step would involve obtaining more details on these lines to find out which one matches [tex]\(\frac{6}{5}\)[/tex]. If any additional details are available, please let me know, and I can assist you further.
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