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

A. line [tex]PQ[/tex]

B. line [tex]LM[/tex]

C. line [tex]JK[/tex]

D. line [tex]NO[/tex]

Answer :

Sure! Let's work through the solution step-by-step to find which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex].

1. Understand Perpendicular Slopes:
- When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line.

2. Find the Negative Reciprocal:
- Start with the given slope: [tex]\(-\frac{5}{6}\)[/tex].
- To find the perpendicular slope, take the negative reciprocal. This means you flip the fraction and change the sign.
- So, the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].

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

Now, to figure out which line (line [tex]\(PQ\)[/tex], line [tex]\(LM\)[/tex], line [tex]\(JK\)[/tex], or line [tex]\(NO\)[/tex]) is perpendicular to the original line, you would need additional information such as the slopes of those lines. Using that information, you would match the slope [tex]\(6/5\)[/tex] to determine which line is perpendicular.

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