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Answer :
To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of a perpendicular line first. Here's how you can do that:
1. Understand what it means for lines to be perpendicular: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This means that to find the slope of a line perpendicular to our given line, you 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, you flip the fraction and change the sign. That means you swap the numerator and the denominator and make it positive (since it's currently negative):
[tex]\[
\text{Reciprocal of } -\frac{5}{6}\text{ is }\frac{6}{5}
\][/tex]
3. Determine the slope of the perpendicular line: The slope of the line that is perpendicular to the one with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Once you have that slope, you would need to check the slopes of the lines JK, LM, NO, and PQ to see which one matches [tex]\(\frac{6}{5}\)[/tex]. The line with this slope will be the one that is perpendicular to the original line.
1. Understand what it means for lines to be perpendicular: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This means that to find the slope of a line perpendicular to our given line, you 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, you flip the fraction and change the sign. That means you swap the numerator and the denominator and make it positive (since it's currently negative):
[tex]\[
\text{Reciprocal of } -\frac{5}{6}\text{ is }\frac{6}{5}
\][/tex]
3. Determine the slope of the perpendicular line: The slope of the line that is perpendicular to the one with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Once you have that slope, you would need to check the slopes of the lines JK, LM, NO, and PQ to see which one matches [tex]\(\frac{6}{5}\)[/tex]. The line with this slope will be the one that is perpendicular to the original line.
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