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Answer :
To solve the problem of finding a line that is perpendicular to a line with a given slope of [tex]\(-\frac{5}{6}\)[/tex], we need to understand the concept of perpendicular slopes.
When a line is perpendicular to another line, the slope of the second line is the negative reciprocal of the slope of the first line. The negative reciprocal of a number [tex]\( m \)[/tex] is [tex]\(-\frac{1}{m}\)[/tex].
Here's the step-by-step solution to find the slope of the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex]:
1. Find the Negative Reciprocal:
The original slope is [tex]\(-\frac{5}{6}\)[/tex]. To find the slope of the line that is perpendicular, calculate the negative reciprocal.
[tex]\[
\text{Perpendicular slope} = -\left(\frac{-1}{-\frac{5}{6}}\right)
\][/tex]
2. Calculate the Perpendicular Slope:
Simplify the expression for the perpendicular slope:
[tex]\[
\text{Perpendicular slope} = \frac{6}{5}
\][/tex]
Therefore, the slope of the line perpendicular to a line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, you would look for which line (JK, LM, NO, PQ) has this slope of [tex]\(\frac{6}{5}\)[/tex] to determine which one is perpendicular to the original line with slope [tex]\(-\frac{5}{6}\)[/tex]. The line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be the perpendicular line. You would need additional information, such as equations or slopes of the given lines, to identify this line correctly.
When a line is perpendicular to another line, the slope of the second line is the negative reciprocal of the slope of the first line. The negative reciprocal of a number [tex]\( m \)[/tex] is [tex]\(-\frac{1}{m}\)[/tex].
Here's the step-by-step solution to find the slope of the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex]:
1. Find the Negative Reciprocal:
The original slope is [tex]\(-\frac{5}{6}\)[/tex]. To find the slope of the line that is perpendicular, calculate the negative reciprocal.
[tex]\[
\text{Perpendicular slope} = -\left(\frac{-1}{-\frac{5}{6}}\right)
\][/tex]
2. Calculate the Perpendicular Slope:
Simplify the expression for the perpendicular slope:
[tex]\[
\text{Perpendicular slope} = \frac{6}{5}
\][/tex]
Therefore, the slope of the line perpendicular to a line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, you would look for which line (JK, LM, NO, PQ) has this slope of [tex]\(\frac{6}{5}\)[/tex] to determine which one is perpendicular to the original line with slope [tex]\(-\frac{5}{6}\)[/tex]. The line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be the perpendicular line. You would need additional information, such as equations or slopes of the given lines, to identify this line correctly.
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