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Answer :
To find a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine what the slope of the perpendicular line would be.
When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. So, if one line has a slope of [tex]\(-\frac{5}{6}\)[/tex], let's call this slope [tex]\(m_1\)[/tex], then the slope of the perpendicular line, [tex]\(m_2\)[/tex], must satisfy the following equation:
[tex]\[
m_1 \times m_2 = -1
\][/tex]
Given:
[tex]\[
m_1 = -\frac{5}{6}
\][/tex]
Substitute this value into the equation:
[tex]\[
-\frac{5}{6} \times m_2 = -1
\][/tex]
To solve for [tex]\(m_2\)[/tex], divide both sides of the equation by [tex]\(-\frac{5}{6}\)[/tex]:
[tex]\[
m_2 = \frac{-1}{-\frac{5}{6}}
\][/tex]
Simplify the expression:
[tex]\[
m_2 = \frac{1}{\frac{5}{6}}
\][/tex]
This is the same as multiplying by the reciprocal:
[tex]\[
m_2 = 1 \times \frac{6}{5}
\][/tex]
[tex]\[
m_2 = \frac{6}{5}
\][/tex]
Therefore, the slope of any line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
To find the specific line (line JK, LM, NO, or PQ) that has a slope of [tex]\(\frac{6}{5}\)[/tex], you would typically need additional information about the slopes of those lines. However, based on the numerical result provided, the correct answer choice is the line with a slope of [tex]\(1.2\)[/tex], which is equivalent to the slope [tex]\(\frac{6}{5}\)[/tex].
When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. So, if one line has a slope of [tex]\(-\frac{5}{6}\)[/tex], let's call this slope [tex]\(m_1\)[/tex], then the slope of the perpendicular line, [tex]\(m_2\)[/tex], must satisfy the following equation:
[tex]\[
m_1 \times m_2 = -1
\][/tex]
Given:
[tex]\[
m_1 = -\frac{5}{6}
\][/tex]
Substitute this value into the equation:
[tex]\[
-\frac{5}{6} \times m_2 = -1
\][/tex]
To solve for [tex]\(m_2\)[/tex], divide both sides of the equation by [tex]\(-\frac{5}{6}\)[/tex]:
[tex]\[
m_2 = \frac{-1}{-\frac{5}{6}}
\][/tex]
Simplify the expression:
[tex]\[
m_2 = \frac{1}{\frac{5}{6}}
\][/tex]
This is the same as multiplying by the reciprocal:
[tex]\[
m_2 = 1 \times \frac{6}{5}
\][/tex]
[tex]\[
m_2 = \frac{6}{5}
\][/tex]
Therefore, the slope of any line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
To find the specific line (line JK, LM, NO, or PQ) that has a slope of [tex]\(\frac{6}{5}\)[/tex], you would typically need additional information about the slopes of those lines. However, based on the numerical result provided, the correct answer choice is the line with a slope of [tex]\(1.2\)[/tex], which is equivalent to the slope [tex]\(\frac{6}{5}\)[/tex].
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