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Answer :
To determine which line is perpendicular to a line that has a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the perpendicular line. Here's a step-by-step solution:
1. Understand Perpendicular Slopes:
- Two lines are perpendicular if their slopes are negative reciprocals of each other.
- If a line has a slope [tex]\(m\)[/tex], then the slope of a line perpendicular to it is [tex]\(-\frac{1}{m}\)[/tex].
2. Given Slope:
- We are given that the slope of the line is [tex]\(-\frac{5}{6}\)[/tex].
3. Find the Negative Reciprocal:
- To find the slope of the perpendicular line, we need to take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{1}{-\frac{5}{6}}\)[/tex].
- Simplify [tex]\(-\frac{1}{-\frac{5}{6}} = \frac{6}{5}\)[/tex].
4. Result:
- The slope of the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Given this result, we now know that any line that has a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. To identify which specific line is perpendicular from the choices provided (line JK, line LM, line NO, line PQ), we would need additional information about the slopes of those lines.
However, based on the calculations, the slope needs to be [tex]\(\frac{6}{5}\)[/tex] for a line to be perpendicular to the given line.
1. Understand Perpendicular Slopes:
- Two lines are perpendicular if their slopes are negative reciprocals of each other.
- If a line has a slope [tex]\(m\)[/tex], then the slope of a line perpendicular to it is [tex]\(-\frac{1}{m}\)[/tex].
2. Given Slope:
- We are given that the slope of the line is [tex]\(-\frac{5}{6}\)[/tex].
3. Find the Negative Reciprocal:
- To find the slope of the perpendicular line, we need to take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{1}{-\frac{5}{6}}\)[/tex].
- Simplify [tex]\(-\frac{1}{-\frac{5}{6}} = \frac{6}{5}\)[/tex].
4. Result:
- The slope of the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Given this result, we now know that any line that has a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. To identify which specific line is perpendicular from the choices provided (line JK, line LM, line NO, line PQ), we would need additional information about the slopes of those lines.
However, based on the calculations, the slope needs to be [tex]\(\frac{6}{5}\)[/tex] for a line to be perpendicular to the given line.
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