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Answer :
To find a line that is perpendicular to another line with a given slope, we need to use the concept of the negative reciprocal of the slope.
Here's a step-by-step guide to determine the slope of a line that is perpendicular to the given line:
1. Identify the slope of the given line: The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
2. Understand the concept of perpendicular slopes: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This means if you're given the slope of one line, the slope of a line perpendicular to it will be the negative reciprocal of the given slope.
3. Calculate the negative reciprocal:
- Start with the original slope, which is [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal involves switching the numerator and denominator and changing the sign. So, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
4. Convert to decimal if necessary: The negative reciprocal [tex]\(\frac{6}{5}\)[/tex] can be expressed in decimal form as [tex]\(1.2\)[/tex].
Therefore, a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] would have a slope of [tex]\(1.2\)[/tex]. To determine which of the lines (JK, LM, NO, or PQ) is perpendicular, we would need the slope of each line to compare. However, the key takeaway here is that the perpendicular slope is [tex]\(1.2\)[/tex].
Here's a step-by-step guide to determine the slope of a line that is perpendicular to the given line:
1. Identify the slope of the given line: The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
2. Understand the concept of perpendicular slopes: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. This means if you're given the slope of one line, the slope of a line perpendicular to it will be the negative reciprocal of the given slope.
3. Calculate the negative reciprocal:
- Start with the original slope, which is [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal involves switching the numerator and denominator and changing the sign. So, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
4. Convert to decimal if necessary: The negative reciprocal [tex]\(\frac{6}{5}\)[/tex] can be expressed in decimal form as [tex]\(1.2\)[/tex].
Therefore, a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] would have a slope of [tex]\(1.2\)[/tex]. To determine which of the lines (JK, LM, NO, or PQ) is perpendicular, we would need the slope of each line to compare. However, the key takeaway here is that the perpendicular slope is [tex]\(1.2\)[/tex].
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