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Answer :
To determine which line is perpendicular to a line with a given slope, we need to find the negative reciprocal of the original slope. The original slope provided is [tex]\(-\frac{5}{6}\)[/tex].
Here's how you can find the slope of the perpendicular line:
1. Identify the Original Slope: The original slope is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the Negative Reciprocal:
- To get the negative reciprocal of a slope, you first take the reciprocal, which means you flip the fraction. So, the reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Then, take the negative of that reciprocal. So, the negative reciprocal of [tex]\(-\frac{6}{5}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Thus, the slope of a line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Since the solutions have determined this perpendicular slope numerically as approximately [tex]\(1.2\)[/tex], you would need to identify which line (NO, LM, JK, or PQ) has a slope of [tex]\(\frac{6}{5}\)[/tex] or 1.2. If given the equations for these lines or if you have a graph or additional information about the slopes of these lines, you can find which line matches this slope. Without this specific information, we can conclude that the line perpendicular to the one with slope [tex]\(-\frac{5}{6}\)[/tex] has a slope of approximately 1.2 or [tex]\(\frac{6}{5}\)[/tex].
Here's how you can find the slope of the perpendicular line:
1. Identify the Original Slope: The original slope is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the Negative Reciprocal:
- To get the negative reciprocal of a slope, you first take the reciprocal, which means you flip the fraction. So, the reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Then, take the negative of that reciprocal. So, the negative reciprocal of [tex]\(-\frac{6}{5}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Thus, the slope of a line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Since the solutions have determined this perpendicular slope numerically as approximately [tex]\(1.2\)[/tex], you would need to identify which line (NO, LM, JK, or PQ) has a slope of [tex]\(\frac{6}{5}\)[/tex] or 1.2. If given the equations for these lines or if you have a graph or additional information about the slopes of these lines, you can find which line matches this slope. Without this specific information, we can conclude that the line perpendicular to the one with slope [tex]\(-\frac{5}{6}\)[/tex] has a slope of approximately 1.2 or [tex]\(\frac{6}{5}\)[/tex].
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