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Answer :
To find the line that is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine the slope of the perpendicular line first. Here's how to do that step-by-step:
1. Understand the Perpendicular Slope Rule: Two lines are perpendicular to each other if the product of their slopes is [tex]\(-1\)[/tex]. This means the slope of one line is the negative reciprocal of the other's slope.
2. Find the Negative Reciprocal: For the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], the negative reciprocal is calculated by flipping the fraction and changing the sign. So:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Change the sign, and it becomes [tex]\(\frac{6}{5}\)[/tex].
3. Convert to Decimal: To make it easier to compare with other lines, convert [tex]\(\frac{6}{5}\)[/tex] to a decimal:
- [tex]\(\frac{6}{5} = 1.2\)[/tex].
4. Compare Slopes: To determine which line is perpendicular, you would compare the slope of each given line (line JK, line 1 M, line NO, line PQ) to see which has a slope of [tex]\(1.2\)[/tex].
Based on this reasoning, the line with a slope of [tex]\(1.2\)[/tex] is the one perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex]. Without knowing the slopes of lines JK, 1 M, NO, and PQ, you would match the calculated slope [tex]\(1.2\)[/tex] to find the correct line.
1. Understand the Perpendicular Slope Rule: Two lines are perpendicular to each other if the product of their slopes is [tex]\(-1\)[/tex]. This means the slope of one line is the negative reciprocal of the other's slope.
2. Find the Negative Reciprocal: For the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], the negative reciprocal is calculated by flipping the fraction and changing the sign. So:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Change the sign, and it becomes [tex]\(\frac{6}{5}\)[/tex].
3. Convert to Decimal: To make it easier to compare with other lines, convert [tex]\(\frac{6}{5}\)[/tex] to a decimal:
- [tex]\(\frac{6}{5} = 1.2\)[/tex].
4. Compare Slopes: To determine which line is perpendicular, you would compare the slope of each given line (line JK, line 1 M, line NO, line PQ) to see which has a slope of [tex]\(1.2\)[/tex].
Based on this reasoning, the line with a slope of [tex]\(1.2\)[/tex] is the one perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex]. Without knowing the slopes of lines JK, 1 M, NO, and PQ, you would match the calculated slope [tex]\(1.2\)[/tex] to find the correct line.
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