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Answer :
To determine which line is perpendicular to a line that has a slope of [tex]\(-\frac{5}{6}\)[/tex], follow these steps:
1. Understand the concept of perpendicular slopes:
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- If one line has a slope [tex]\(m\)[/tex], then the slope of a line perpendicular to it will be the negative reciprocal of [tex]\(m\)[/tex].
2. Find the negative reciprocal of the given slope:
- The given slope is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, you take the reciprocal of the slope and then change the sign.
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- The negative reciprocal of [tex]\(-\frac{6}{5}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
3. Interpret the numerical result:
- The result from the given information is that the slope of a line perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex].
4. Comparing slopes:
- Convert the slope [tex]\(1.2\)[/tex] back to a fraction if necessary for clarity: [tex]\(1.2\)[/tex] can be written as [tex]\(\frac{6}{5}\)[/tex].
From the calculations above, a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of [tex]\(1.2\)[/tex] (or [tex]\(\frac{6}{5}\)[/tex]).
Therefore, you should identify in the options provided (line JK, line LM, line NO, line PQ) a line that has this slope to determine which is perpendicular.
Unfortunately, without the slopes for these specific lines (JK, LM, NO, PQ) provided in the question, we can't explicitly identify which specific line is perpendicular. However, conceptually, you now know the slope to look for!
1. Understand the concept of perpendicular slopes:
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- If one line has a slope [tex]\(m\)[/tex], then the slope of a line perpendicular to it will be the negative reciprocal of [tex]\(m\)[/tex].
2. Find the negative reciprocal of the given slope:
- The given slope is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, you take the reciprocal of the slope and then change the sign.
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- The negative reciprocal of [tex]\(-\frac{6}{5}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
3. Interpret the numerical result:
- The result from the given information is that the slope of a line perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex].
4. Comparing slopes:
- Convert the slope [tex]\(1.2\)[/tex] back to a fraction if necessary for clarity: [tex]\(1.2\)[/tex] can be written as [tex]\(\frac{6}{5}\)[/tex].
From the calculations above, a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of [tex]\(1.2\)[/tex] (or [tex]\(\frac{6}{5}\)[/tex]).
Therefore, you should identify in the options provided (line JK, line LM, line NO, line PQ) a line that has this slope to determine which is perpendicular.
Unfortunately, without the slopes for these specific lines (JK, LM, NO, PQ) provided in the question, we can't explicitly identify which specific line is perpendicular. However, conceptually, you now know the slope to look for!
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