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Answer :
To find a line perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine the negative reciprocal of this slope.
Here's a step-by-step explanation:
1. Understand the Concept of Negative Reciprocal:
- When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
- To find a slope that is perpendicular, take the negative reciprocal of the given slope.
2. Calculate the Negative Reciprocal:
- The given slope is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, first, invert the fraction to get [tex]\(\frac{6}{5}\)[/tex].
- Then, change the sign, so the negative reciprocal becomes [tex]\( \frac{6}{5} \)[/tex].
3. Interpret the Result:
- A line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
- Alternatively, [tex]\(\frac{6}{5}\)[/tex] can also be expressed as a decimal, which is [tex]\(1.2\)[/tex].
Therefore, the slope of a line that is perpendicular to the original line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex]. Now, you can check which of the given lines (line JK, line LM, line NO, or line PQ) has this slope to determine which one is perpendicular to the original line.
Here's a step-by-step explanation:
1. Understand the Concept of Negative Reciprocal:
- When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
- To find a slope that is perpendicular, take the negative reciprocal of the given slope.
2. Calculate the Negative Reciprocal:
- The given slope is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, first, invert the fraction to get [tex]\(\frac{6}{5}\)[/tex].
- Then, change the sign, so the negative reciprocal becomes [tex]\( \frac{6}{5} \)[/tex].
3. Interpret the Result:
- A line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
- Alternatively, [tex]\(\frac{6}{5}\)[/tex] can also be expressed as a decimal, which is [tex]\(1.2\)[/tex].
Therefore, the slope of a line that is perpendicular to the original line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex]. Now, you can check which of the given lines (line JK, line LM, line NO, or line PQ) has this slope to determine which one is perpendicular to the original line.
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