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Answer :
To determine which line is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the perpendicular line. Here's how:
1. Understanding Perpendicular Slopes: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. In simple terms, if one line has a slope [tex]\(m_1\)[/tex], the perpendicular line will have a slope [tex]\(m_2\)[/tex] such that [tex]\(m_1 \times m_2 = -1\)[/tex].
2. Finding the Perpendicular Slope: Given the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], the perpendicular slope can be found by taking the negative reciprocal of the given slope.
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Changing the sign gives the perpendicular slope, which is [tex]\(\frac{6}{5}\)[/tex].
3. Conclusion: The slope of the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex] or 1.2 when converted to a decimal.
Therefore, the line that is perpendicular to the given line will have a slope of 1.2. You would then match this slope with the slopes of lines JK, LM, NO, and PQ to find the correct line.
1. Understanding Perpendicular Slopes: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. In simple terms, if one line has a slope [tex]\(m_1\)[/tex], the perpendicular line will have a slope [tex]\(m_2\)[/tex] such that [tex]\(m_1 \times m_2 = -1\)[/tex].
2. Finding the Perpendicular Slope: Given the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], the perpendicular slope can be found by taking the negative reciprocal of the given slope.
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Changing the sign gives the perpendicular slope, which is [tex]\(\frac{6}{5}\)[/tex].
3. Conclusion: The slope of the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex] or 1.2 when converted to a decimal.
Therefore, the line that is perpendicular to the given line will have a slope of 1.2. You would then match this slope with the slopes of lines JK, LM, NO, and PQ to find the correct line.
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