To determine which line is perpendicular to a given line with a specific slope, we need to find the slope of the perpendicular line.
Here is a detailed step-by-step solution:
1. Identify the slope of the given line:
The given line has a slope of [tex]\(-\frac{5}{6}\)[/tex].
2. Find the slope of the perpendicular line:
Perpendicular lines have slopes that are negative reciprocals of each other. This means if a line has a slope [tex]\(m\)[/tex], the perpendicular line will have a slope [tex]\(-\frac{1}{m}\)[/tex].
3. Calculate the negative reciprocal:
The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
- To find the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex], we first take the reciprocal:
[tex]\[
\text{Reciprocal of } -\frac{5}{6} \text{ is } \frac{6}{5}.
\][/tex]
- Next, we change the sign:
[tex]\[
-\left(\frac{6}{5}\right) = \frac{6}{5}.
\][/tex]
4. Interpret the result:
The slope of the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Given this information, any line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex]. To identify the specific line (JK, LM, NO, or PQ), we would need to know the slopes of these lines. Since the problem doesn't provide this information, we conclude that the general criteria for a perpendicular line have been met by identifying the slope of the perpendicular line as [tex]\(\frac{6}{5}\)[/tex].
