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Answer :
Sure! 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 line that would be perpendicular to this given line.
1. Understand Perpendicular Slopes: When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line.
2. Calculate the Negative Reciprocal:
- The original slope of the line is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, you first take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex], which is [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to find the negative reciprocal: [tex]\( \frac{6}{5} \)[/tex].
3. Converting to Decimal for Comparison:
- The slope [tex]\(\frac{6}{5}\)[/tex] as a decimal is [tex]\(1.2\)[/tex].
Now, you would compare [tex]\(1.2\)[/tex] with the slopes of the lines JK, LM, NO, and PQ. The line with a slope of [tex]\(1.2\)[/tex] will be perpendicular to the original line. If you have the slope values for these lines, you can identify the correct line. If not, this information should be used in conjunction with the slopes to find the correct line.
1. Understand Perpendicular Slopes: When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line.
2. Calculate the Negative Reciprocal:
- The original slope of the line is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal, you first take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex], which is [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to find the negative reciprocal: [tex]\( \frac{6}{5} \)[/tex].
3. Converting to Decimal for Comparison:
- The slope [tex]\(\frac{6}{5}\)[/tex] as a decimal is [tex]\(1.2\)[/tex].
Now, you would compare [tex]\(1.2\)[/tex] with the slopes of the lines JK, LM, NO, and PQ. The line with a slope of [tex]\(1.2\)[/tex] will be perpendicular to the original line. If you have the slope values for these lines, you can identify the correct line. If not, this information should be used in conjunction with the slopes to find the correct line.
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