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Answer :
To find the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine the slope of the perpendicular line. Here's how we can do it:
1. Understand Perpendicular Slopes:
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- Therefore, the slope of the line perpendicular to a line with slope [tex]\(m\)[/tex] is the negative reciprocal of [tex]\(m\)[/tex].
2. Find the Negative Reciprocal:
- Given the original slope is [tex]\(-\frac{5}{6}\)[/tex], we find the negative reciprocal by flipping the fraction and changing the sign.
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- The negative reciprocal would then be [tex]\(\frac{6}{5}\)[/tex].
3. Convert Fraction to Decimal:
- Converting [tex]\(\frac{6}{5}\)[/tex] to a decimal gives us [tex]\(1.2\)[/tex].
So, the slope of the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex]. You would look for the line among the options (JK, LM, NO, PQ) that has a slope of [tex]\(1.2\)[/tex] to find the correct answer.
1. Understand Perpendicular Slopes:
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- Therefore, the slope of the line perpendicular to a line with slope [tex]\(m\)[/tex] is the negative reciprocal of [tex]\(m\)[/tex].
2. Find the Negative Reciprocal:
- Given the original slope is [tex]\(-\frac{5}{6}\)[/tex], we find the negative reciprocal by flipping the fraction and changing the sign.
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- The negative reciprocal would then be [tex]\(\frac{6}{5}\)[/tex].
3. Convert Fraction to Decimal:
- Converting [tex]\(\frac{6}{5}\)[/tex] to a decimal gives us [tex]\(1.2\)[/tex].
So, the slope of the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex]. You would look for the line among the options (JK, LM, NO, PQ) that has a slope of [tex]\(1.2\)[/tex] to find the correct answer.
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