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Answer :
To find the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find its perpendicular slope. Here's how it works:
1. Understanding Perpendicular Slopes: For two lines to be perpendicular to each other, the product of their slopes must be [tex]\(-1\)[/tex]. This means if you multiply the slope of the first line by the slope of the second line and get [tex]\(-1\)[/tex], the lines are perpendicular.
2. Find the Perpendicular Slope: If the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], let's denote this as [tex]\(m_1\)[/tex]. To find the slope of the line perpendicular to it, let's denote the perpendicular slope as [tex]\(m_2\)[/tex]. The relationship is given by:
[tex]\[
m_1 \times m_2 = -1
\][/tex]
Plugging in the given slope:
[tex]\[
-\frac{5}{6} \times m_2 = -1
\][/tex]
3. Solve for [tex]\(m_2\)[/tex]:
[tex]\[
m_2 = \frac{6}{5}
\][/tex]
The slope of the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, you would need to check the slopes of lines JK, LM, NO, and PQ to see which one has a slope of [tex]\(\frac{6}{5}\)[/tex]. The line with this slope will be the one perpendicular to the original line.
1. Understanding Perpendicular Slopes: For two lines to be perpendicular to each other, the product of their slopes must be [tex]\(-1\)[/tex]. This means if you multiply the slope of the first line by the slope of the second line and get [tex]\(-1\)[/tex], the lines are perpendicular.
2. Find the Perpendicular Slope: If the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], let's denote this as [tex]\(m_1\)[/tex]. To find the slope of the line perpendicular to it, let's denote the perpendicular slope as [tex]\(m_2\)[/tex]. The relationship is given by:
[tex]\[
m_1 \times m_2 = -1
\][/tex]
Plugging in the given slope:
[tex]\[
-\frac{5}{6} \times m_2 = -1
\][/tex]
3. Solve for [tex]\(m_2\)[/tex]:
[tex]\[
m_2 = \frac{6}{5}
\][/tex]
The slope of the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, you would need to check the slopes of lines JK, LM, NO, and PQ to see which one has a slope of [tex]\(\frac{6}{5}\)[/tex]. The line with this slope will be the one perpendicular to the original line.
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