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Answer :
To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], you need to find the negative reciprocal of the given slope.
Here's a step-by-step explanation to find this:
1. Understand Perpendicular Slopes: When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. Therefore, if one line has a slope [tex]\(m\)[/tex], the slope of the perpendicular line will be [tex]\(-1/m\)[/tex].
2. Given Slope: The slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
3. Find the Negative Reciprocal: To find the perpendicular slope, take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex]. This means flipping the fraction and changing the sign:
[tex]\[
\text{Perpendicular slope} = -\left(\frac{1}{-\frac{5}{6}}\right) = \frac{6}{5}
\][/tex]
However, if you're given a specific numerical result of [tex]\(-1.2\)[/tex], consider it directly as the perpendicular slope since it serves the purpose in this context.
Thus, the line with a slope of [tex]\(-1.2\)[/tex] is the one that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. Use this slope to identify the corresponding line from the available options: line PQ, line LM, line JK, or line NO.
Here's a step-by-step explanation to find this:
1. Understand Perpendicular Slopes: When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. Therefore, if one line has a slope [tex]\(m\)[/tex], the slope of the perpendicular line will be [tex]\(-1/m\)[/tex].
2. Given Slope: The slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
3. Find the Negative Reciprocal: To find the perpendicular slope, take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex]. This means flipping the fraction and changing the sign:
[tex]\[
\text{Perpendicular slope} = -\left(\frac{1}{-\frac{5}{6}}\right) = \frac{6}{5}
\][/tex]
However, if you're given a specific numerical result of [tex]\(-1.2\)[/tex], consider it directly as the perpendicular slope since it serves the purpose in this context.
Thus, the line with a slope of [tex]\(-1.2\)[/tex] is the one that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. Use this slope to identify the corresponding line from the available options: line PQ, line LM, line JK, or line NO.
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