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Answer :
To find a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to identify the slope of the perpendicular line.
1. Understand Perpendicular Slopes: Lines that are perpendicular to each other have slopes that are negative reciprocals. This means that if you multiply the slopes of two perpendicular lines together, the result will be [tex]\(-1\)[/tex].
2. Calculate the Negative Reciprocal:
- The original slope is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, you flip the fraction and change the sign. This changes the slope to [tex]\(\frac{6}{5}\)[/tex].
- Therefore, the slope of the perpendicular line is [tex]\(\frac{6}{5}\)[/tex] or 1.2.
3. Result: A line with a slope of 1.2 will be perpendicular to a line with the slope of [tex]\(-\frac{5}{6}\)[/tex].
So, the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] must have a slope of 1.2. You would need additional information to determine which specific line (e.g., JK, LM, NO, or PQ) has this slope based on actual line equations or points.
1. Understand Perpendicular Slopes: Lines that are perpendicular to each other have slopes that are negative reciprocals. This means that if you multiply the slopes of two perpendicular lines together, the result will be [tex]\(-1\)[/tex].
2. Calculate the Negative Reciprocal:
- The original slope is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, you flip the fraction and change the sign. This changes the slope to [tex]\(\frac{6}{5}\)[/tex].
- Therefore, the slope of the perpendicular line is [tex]\(\frac{6}{5}\)[/tex] or 1.2.
3. Result: A line with a slope of 1.2 will be perpendicular to a line with the slope of [tex]\(-\frac{5}{6}\)[/tex].
So, the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] must have a slope of 1.2. You would need additional information to determine which specific line (e.g., JK, LM, NO, or PQ) has this slope based on actual line equations or points.
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