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Which line is perpendicular to a line that has a slope of [tex]$-\frac{5}{6}$[/tex]?

A. line JK
B. line LM
C. line NO
D. line PQ

Answer :

To determine which line is perpendicular to a given line, we need to find the perpendicular slope. For a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], the slope of a line that is perpendicular to it will be the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].

Here's how to find it step-by-step:

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

2. Find the negative reciprocal:
- First, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex]. The reciprocal means flipping the fraction, so the reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Then, take the negative of this reciprocal. The negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex] (because taking the negative of a negative number gives a positive result).

3. Determine which line has this slope: In this case, we'd need the equations or slopes of lines JK, LM, NO, and PQ to see which one has a slope of [tex]\(\frac{6}{5}\)[/tex].

Without the equations or additional information about lines JK, LM, NO, and PQ, we cannot determine which line is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. Additional information is needed to match these lines with the slope [tex]\(\frac{6}{5}\)[/tex].

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