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Answer :
To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope that would make a line perpendicular to this given line.
### Step-by-step solution:
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.
2. Find the Negative Reciprocal:
- If the original slope of the line is [tex]\(-\frac{5}{6}\)[/tex], then the slope of a line that is perpendicular to it will be the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal means that you invert the fraction and change its sign.
3. Calculate the Perpendicular Slope:
- The negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex]. Since the original slope is negative, the perpendicular slope will be positive.
4. Result:
- The slope of the line that is perpendicular to one with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex] or [tex]\(1.2\)[/tex].
Now, you would compare this result with the slopes of the given lines (line JK, line LM, line NO, line PQ) based on their equations to find which line has the slope [tex]\(1.2\)[/tex]. Unfortunately, without the information on the slopes or equations of lines JK, LM, NO, and PQ, we cannot identify which line has the slope of [tex]\(1.2\)[/tex]. You would need to verify each line's equation to confirm which one is perpendicular.
### Step-by-step solution:
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.
2. Find the Negative Reciprocal:
- If the original slope of the line is [tex]\(-\frac{5}{6}\)[/tex], then the slope of a line that is perpendicular to it will be the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
- The negative reciprocal means that you invert the fraction and change its sign.
3. Calculate the Perpendicular Slope:
- The negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex]. Since the original slope is negative, the perpendicular slope will be positive.
4. Result:
- The slope of the line that is perpendicular to one with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex] or [tex]\(1.2\)[/tex].
Now, you would compare this result with the slopes of the given lines (line JK, line LM, line NO, line PQ) based on their equations to find which line has the slope [tex]\(1.2\)[/tex]. Unfortunately, without the information on the slopes or equations of lines JK, LM, NO, and PQ, we cannot identify which line has the slope of [tex]\(1.2\)[/tex]. You would need to verify each line's equation to confirm which one is perpendicular.
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