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Answer :
To find which line is perpendicular to a line that has a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine the perpendicular slope.
Here's how we can do it step-by-step:
1. Understand Perpendicular Slopes: Perpendicular lines have slopes that are negative reciprocals of each other. This means if you flip the numerator and denominator of a fraction and change the sign, you'll get the negative reciprocal.
2. Find the Negative Reciprocal: Take the slope [tex]\(-\frac{5}{6}\)[/tex] and find its negative reciprocal.
- 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 to Decimal Form: Convert [tex]\(\frac{6}{5}\)[/tex] to decimal form.
- [tex]\(\frac{6}{5} = 1.2\)[/tex]
Therefore, the slope of a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex]. Now you need to check which of the lines provided (line JK, line LM, line NO, line PQ) has a slope of [tex]\(1.2\)[/tex].
Here's how we can do it step-by-step:
1. Understand Perpendicular Slopes: Perpendicular lines have slopes that are negative reciprocals of each other. This means if you flip the numerator and denominator of a fraction and change the sign, you'll get the negative reciprocal.
2. Find the Negative Reciprocal: Take the slope [tex]\(-\frac{5}{6}\)[/tex] and find its negative reciprocal.
- 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 to Decimal Form: Convert [tex]\(\frac{6}{5}\)[/tex] to decimal form.
- [tex]\(\frac{6}{5} = 1.2\)[/tex]
Therefore, the slope of a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex]. Now you need to check which of the lines provided (line JK, line LM, line NO, line PQ) has a slope of [tex]\(1.2\)[/tex].
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