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Answer :
To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], follow these steps:
1. Understand the concept of perpendicular slopes:
- The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. The negative reciprocal of a number [tex]\( m \)[/tex] is [tex]\( -\frac{1}{m} \)[/tex].
2. Find the perpendicular slope:
- Given the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], we need to find the negative reciprocal of this given slope.
- To find the negative reciprocal, flip the fraction and change the sign. Thus, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
3. Evaluate the result:
- Let's convert the fraction [tex]\(\frac{6}{5}\)[/tex] into a decimal for better clarity. [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]. The line that has this slope is the one that is perpendicular.
Given the options (line JK, line LM, line NO, line PQ), we need to check which of these lines has a slope of [tex]\(1.2\)[/tex] to answer the question correctly.
1. Understand the concept of perpendicular slopes:
- The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. The negative reciprocal of a number [tex]\( m \)[/tex] is [tex]\( -\frac{1}{m} \)[/tex].
2. Find the perpendicular slope:
- Given the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], we need to find the negative reciprocal of this given slope.
- To find the negative reciprocal, flip the fraction and change the sign. Thus, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
3. Evaluate the result:
- Let's convert the fraction [tex]\(\frac{6}{5}\)[/tex] into a decimal for better clarity. [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]. The line that has this slope is the one that is perpendicular.
Given the options (line JK, line LM, line NO, line PQ), we need to check which of these lines has a slope of [tex]\(1.2\)[/tex] to answer the question correctly.
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