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Answer :
Sure, let's understand how to find the line that is perpendicular to another line given its slope.
1. Understand the concept of perpendicular slopes:
When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line.
2. Identify the given slope:
We are given a slope of [tex]\(-\frac{5}{6}\)[/tex].
3. Find the negative reciprocal:
To find the negative reciprocal, we'll:
- First, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex], flipping the fraction: [tex]\(-\frac{5}{6}\)[/tex] becomes [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to get the negative reciprocal. Since [tex]\(-\frac{6}{5}\)[/tex] is already negative, the reciprocal will be [tex]\(\frac{6}{5}\)[/tex].
So, a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
Unfortunately, without additional information about the slopes of the lines JK, LM, NO, and PQ, we cannot pinpoint which line exactly has the slope [tex]\(\frac{6}{5}\)[/tex]. However, now you know that the line you are looking for must have a slope of [tex]\(\frac{6}{5}\)[/tex].
If you have any further data on the slopes of the lines mentioned, you could then match this calculated slope to identify the correct line.
1. Understand the concept of perpendicular slopes:
When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line.
2. Identify the given slope:
We are given a slope of [tex]\(-\frac{5}{6}\)[/tex].
3. Find the negative reciprocal:
To find the negative reciprocal, we'll:
- First, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex], flipping the fraction: [tex]\(-\frac{5}{6}\)[/tex] becomes [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to get the negative reciprocal. Since [tex]\(-\frac{6}{5}\)[/tex] is already negative, the reciprocal will be [tex]\(\frac{6}{5}\)[/tex].
So, a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
Unfortunately, without additional information about the slopes of the lines JK, LM, NO, and PQ, we cannot pinpoint which line exactly has the slope [tex]\(\frac{6}{5}\)[/tex]. However, now you know that the line you are looking for must have a slope of [tex]\(\frac{6}{5}\)[/tex].
If you have any further data on the slopes of the lines mentioned, you could then match this calculated slope to identify the correct line.
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