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Answer :
To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the perpendicular slope.
1. Understand the concept of perpendicular slopes:
- When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
- Therefore, the slope of a line perpendicular to one with slope [tex]\(m\)[/tex] is the negative reciprocal of [tex]\(m\)[/tex].
2. Find the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex]:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Negate this reciprocal to find the perpendicular slope: [tex]\(\frac{6}{5}\)[/tex].
3. Convert the slope to a decimal for easier comparison:
- [tex]\(\frac{6}{5}\)[/tex] as a decimal is 1.2.
The line that has a slope of 1.2 is the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. Be sure to check which line (JK, LM, NO, or PQ) has this slope of 1.2 to identify the correct answer.
1. Understand the concept of perpendicular slopes:
- When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
- Therefore, the slope of a line perpendicular to one with slope [tex]\(m\)[/tex] is the negative reciprocal of [tex]\(m\)[/tex].
2. Find the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex]:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Negate this reciprocal to find the perpendicular slope: [tex]\(\frac{6}{5}\)[/tex].
3. Convert the slope to a decimal for easier comparison:
- [tex]\(\frac{6}{5}\)[/tex] as a decimal is 1.2.
The line that has a slope of 1.2 is the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. Be sure to check which line (JK, LM, NO, or PQ) has this slope of 1.2 to identify the correct answer.
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