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 negative reciprocal of that slope. A line that is perpendicular will have a slope that is the opposite reciprocal of the original line's slope.

Let's follow these steps:

1. Identify the Original Slope: The original slope given is [tex]\(-\frac{5}{6}\)[/tex].

2. Find the Negative Reciprocal:
- The reciprocal of a slope [tex]\(-\frac{5}{6}\)[/tex] is obtained by flipping the fraction, which gives us [tex]\(\frac{6}{5}\)[/tex].
- To find the negative reciprocal, we change the sign as well: [tex]\(\frac{6}{5}\)[/tex].

3. Interpret the Result: The slope of the line that is perpendicular to the given line is [tex]\(\frac{6}{5}\)[/tex].

If you have a list of lines, such as line JK, line LM, line NO, and line PQ, you'll need to determine their respective slopes. The line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be the one that is perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex].

Check which one of these lines matches the calculated slope to find your perpendicular line.

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