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Answer :
To find which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine the slope of a line that would be perpendicular to it. Here's how you can do this:
1. Understand the Concept of Perpendicular Slopes:
- When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
- If the slope of one line is [tex]\(m\)[/tex], then the slope of the line perpendicular to it is the negative reciprocal of [tex]\(m\)[/tex].
2. Identify the Slope Provided:
- The given slope is [tex]\(-\frac{5}{6}\)[/tex].
3. Calculate the Perpendicular Slope:
- To find the negative reciprocal, you invert the fraction and change the sign.
- So, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Therefore, the slope of the line that is perpendicular to the given line is [tex]\(\frac{6}{5}\)[/tex]. To determine which of the lines [tex]\(JK\)[/tex], [tex]\(LM\)[/tex], [tex]\(NO\)[/tex], or [tex]\(PQ\)[/tex] has this slope, you would need information on the slopes of these lines provided through their equations or otherwise. Based on the numerical result stated (1.2), [tex]\(\frac{6}{5}\)[/tex] indeed translates to 1.2. So, the line with a slope of 1.2 is the one perpendicular to the given line with slope [tex]\(-\frac{5}{6}\)[/tex].
1. Understand the Concept of Perpendicular Slopes:
- When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
- If the slope of one line is [tex]\(m\)[/tex], then the slope of the line perpendicular to it is the negative reciprocal of [tex]\(m\)[/tex].
2. Identify the Slope Provided:
- The given slope is [tex]\(-\frac{5}{6}\)[/tex].
3. Calculate the Perpendicular Slope:
- To find the negative reciprocal, you invert the fraction and change the sign.
- So, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Therefore, the slope of the line that is perpendicular to the given line is [tex]\(\frac{6}{5}\)[/tex]. To determine which of the lines [tex]\(JK\)[/tex], [tex]\(LM\)[/tex], [tex]\(NO\)[/tex], or [tex]\(PQ\)[/tex] has this slope, you would need information on the slopes of these lines provided through their equations or otherwise. Based on the numerical result stated (1.2), [tex]\(\frac{6}{5}\)[/tex] indeed translates to 1.2. So, the line with a slope of 1.2 is the one perpendicular to the given line with slope [tex]\(-\frac{5}{6}\)[/tex].
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