To determine which line is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the perpendicular line. The key is understanding the relationship between the slopes of perpendicular lines.
The slopes of two perpendicular lines are negative reciprocals of each other. This means if one line has a slope [tex]\( m \)[/tex], the perpendicular line's slope will be [tex]\( -\frac{1}{m} \)[/tex].
Given:
1. The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
To find the slope of the line perpendicular to this:
1. Take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
The negative reciprocal formula states:
[tex]\[ \text{slope of the perpendicular line} = -\left(\frac{1}{-\frac{5}{6}}\right) \][/tex]
Simplifying this:
[tex]\[ -\left(\frac{1}{-\frac{5}{6}}\right) = -\left(-\frac{6}{5}\right) = \frac{6}{5} \][/tex]
So, 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].
Thus, whichever of the lines JK, LM, NO, or PQ that has a slope of [tex]\(\frac{6}{5}\)[/tex] would be the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
In conclusion, the line perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of [tex]\(\frac{6}{5}\)[/tex].
