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Answer :
To find a line that is perpendicular to a given line, we need to determine the slope of the perpendicular line.
1. Identify the Slope of the Original Line:
- The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the Slope of the Perpendicular Line:
- The slope of a line that is perpendicular to another is the negative reciprocal of the original line's slope.
- To find the negative reciprocal, first, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex], which is [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to get [tex]\(\frac{6}{5}\)[/tex]. This means a line with a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the original line.
Therefore, the line that has a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the line with the slope of [tex]\(-\frac{5}{6}\)[/tex]. To find which of the lines—JK, LM, NO, or PQ—has this slope, check the given options to see which one includes it.
When considering problems like these, it’s important to note the relationship between slopes: perpendicular slopes are always negative reciprocals of one another.
1. Identify the Slope of the Original Line:
- The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the Slope of the Perpendicular Line:
- The slope of a line that is perpendicular to another is the negative reciprocal of the original line's slope.
- To find the negative reciprocal, first, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex], which is [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to get [tex]\(\frac{6}{5}\)[/tex]. This means a line with a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the original line.
Therefore, the line that has a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the line with the slope of [tex]\(-\frac{5}{6}\)[/tex]. To find which of the lines—JK, LM, NO, or PQ—has this slope, check the given options to see which one includes it.
When considering problems like these, it’s important to note the relationship between slopes: perpendicular slopes are always negative reciprocals of one another.
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