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Answer :
To find which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine the slope of the perpendicular line.
When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. Therefore, to find the slope of the line that is perpendicular to the one with a slope of [tex]\(-\frac{5}{6}\)[/tex], we take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
Here are the steps:
1. Find the reciprocal of the original slope:
The original slope is [tex]\(-\frac{5}{6}\)[/tex]. The reciprocal is found by flipping the numerator and denominator. So, the reciprocal is [tex]\(-\frac{6}{5}\)[/tex].
2. Change the sign to find the perpendicular slope:
The negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex], but we must remember to change the sign. Therefore, the perpendicular slope becomes [tex]\(\frac{6}{5}\)[/tex].
3. Convert the slope to decimal form for easier comparison:
[tex]\(\frac{6}{5}\)[/tex] in decimal form is [tex]\(1.2\)[/tex].
Now, given a list of lines, you would choose the line having a slope of [tex]\(1.2\)[/tex] because that slope is perpendicular to the original line with slope [tex]\(-\frac{5}{6}\)[/tex].
When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. Therefore, to find the slope of the line that is perpendicular to the one with a slope of [tex]\(-\frac{5}{6}\)[/tex], we take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
Here are the steps:
1. Find the reciprocal of the original slope:
The original slope is [tex]\(-\frac{5}{6}\)[/tex]. The reciprocal is found by flipping the numerator and denominator. So, the reciprocal is [tex]\(-\frac{6}{5}\)[/tex].
2. Change the sign to find the perpendicular slope:
The negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex], but we must remember to change the sign. Therefore, the perpendicular slope becomes [tex]\(\frac{6}{5}\)[/tex].
3. Convert the slope to decimal form for easier comparison:
[tex]\(\frac{6}{5}\)[/tex] in decimal form is [tex]\(1.2\)[/tex].
Now, given a list of lines, you would choose the line having a slope of [tex]\(1.2\)[/tex] because that slope is perpendicular to the original line with slope [tex]\(-\frac{5}{6}\)[/tex].
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