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Answer :
To determine which line is perpendicular to a line that has a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the perpendicular line.
1. Understand Perpendicular Slopes: Two lines are perpendicular when the product of their slopes is [tex]\(-1\)[/tex]. This means that the slope of a line perpendicular to another is the negative reciprocal of the original line's slope.
2. Find the Negative Reciprocal:
- The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
- To find the slope of the perpendicular line, we take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
3. Calculate the Negative Reciprocal:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Since we need the negative reciprocal, we change the sign, resulting in a slope of [tex]\(\frac{6}{5}\)[/tex].
Therefore, the slope of the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, if you have multiple lines (like line JK, LM, NO, PQ), you would compare this perpendicular slope ([tex]\(\frac{6}{5}\)[/tex]) to the slopes of the given lines to determine which one matches. Only the line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be perpendicular to the original line. Make sure to have the slopes of those lines on hand to match accordingly.
1. Understand Perpendicular Slopes: Two lines are perpendicular when the product of their slopes is [tex]\(-1\)[/tex]. This means that the slope of a line perpendicular to another is the negative reciprocal of the original line's slope.
2. Find the Negative Reciprocal:
- The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
- To find the slope of the perpendicular line, we take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
3. Calculate the Negative Reciprocal:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Since we need the negative reciprocal, we change the sign, resulting in a slope of [tex]\(\frac{6}{5}\)[/tex].
Therefore, the slope of the line that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, if you have multiple lines (like line JK, LM, NO, PQ), you would compare this perpendicular slope ([tex]\(\frac{6}{5}\)[/tex]) to the slopes of the given lines to determine which one matches. Only the line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be perpendicular to the original line. Make sure to have the slopes of those lines on hand to match accordingly.
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