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Answer :
Sure, I'd be happy to help!
To find which line is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to understand the relationship between the slopes of perpendicular lines. Here are the steps:
### Step 1: Understand the Relationship
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- This means that if one line has a slope [tex]\(m\)[/tex], then the slope of a line perpendicular to it would be [tex]\(-\frac{1}{m}\)[/tex].
### Step 2: Calculate the Perpendicular Slope
Given the slope of the line:
[tex]\[ m = -\frac{5}{6} \][/tex]
To find the slope of the perpendicular line ([tex]\(m_{\perp}\)[/tex]), we take the negative reciprocal:
[tex]\[ m_{\perp} = -\frac{1}{m} \][/tex]
### Step 3: Perform the Calculation
Let's compute this:
[tex]\[ m_{\perp} = -\frac{1}{-\frac{5}{6}} \][/tex]
[tex]\[ m_{\perp} = \frac{6}{5} \][/tex]
So, the slope of the line that is perpendicular to the given line is [tex]\(\frac{6}{5}\)[/tex].
### Step 4: Check the Options
Since no specific details are provided about lines JK, LM, NO, and PQ, the key takeaway is that the perpendicular line to the one with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
Therefore, any of these lines would be correct if they have a slope of [tex]\(\frac{6}{5}\)[/tex].
If we had more information about the specific slopes of lines JK, LM, NO, and PQ, we could identify the exact line among them. For now, with the information provided, we know the perpendicular slope we are looking for.
I hope this helps! Let me know if you have any more questions.
To find which line is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to understand the relationship between the slopes of perpendicular lines. Here are the steps:
### Step 1: Understand the Relationship
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- This means that if one line has a slope [tex]\(m\)[/tex], then the slope of a line perpendicular to it would be [tex]\(-\frac{1}{m}\)[/tex].
### Step 2: Calculate the Perpendicular Slope
Given the slope of the line:
[tex]\[ m = -\frac{5}{6} \][/tex]
To find the slope of the perpendicular line ([tex]\(m_{\perp}\)[/tex]), we take the negative reciprocal:
[tex]\[ m_{\perp} = -\frac{1}{m} \][/tex]
### Step 3: Perform the Calculation
Let's compute this:
[tex]\[ m_{\perp} = -\frac{1}{-\frac{5}{6}} \][/tex]
[tex]\[ m_{\perp} = \frac{6}{5} \][/tex]
So, the slope of the line that is perpendicular to the given line is [tex]\(\frac{6}{5}\)[/tex].
### Step 4: Check the Options
Since no specific details are provided about lines JK, LM, NO, and PQ, the key takeaway is that the perpendicular line to the one with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
Therefore, any of these lines would be correct if they have a slope of [tex]\(\frac{6}{5}\)[/tex].
If we had more information about the specific slopes of lines JK, LM, NO, and PQ, we could identify the exact line among them. For now, with the information provided, we know the perpendicular slope we are looking for.
I hope this helps! Let me know if you have any more questions.
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