To determine which line is perpendicular to a line with a given slope, we need to find the slope of the line that is perpendicular to it. When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex].
Let's denote the slope of the given line by [tex]\( m \)[/tex]. In this case, the given slope [tex]\( m \)[/tex] is [tex]\( -\frac{5}{6} \)[/tex].
To find the slope of the line that is perpendicular to this one, we take the negative reciprocal of the given slope. Here are the steps:
1. Start with the given slope: [tex]\( m = -\frac{5}{6} \)[/tex].
2. Find the negative reciprocal of [tex]\( m \)[/tex]:
- The reciprocal of [tex]\( -\frac{5}{6} \)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].
- Since we need the negative reciprocal, we change the sign: [tex]\(- \left(-\frac{6}{5} \right) = \frac{6}{5} \)[/tex].
So, the slope of the line perpendicular to the given line with a slope of [tex]\( -\frac{5}{6} \)[/tex] is [tex]\( \frac{6}{5} \)[/tex].
Therefore, the line that is perpendicular to the line with a slope of [tex]\( -\frac{5}{6} \)[/tex] would be the line with a slope of [tex]\( 1.2 \)[/tex].
Consequently, to find which line among JK, LM, NO, and PQ is perpendicular to the given line, we look for the line that has a slope of [tex]\( 1.2 \)[/tex].
Based on our solution and the provided answer, the correct line cannot be directly derived from the given options without additional information about the slopes of these lines. However, we've determined that a perpendicular line would indeed have a slope of [tex]\( 1.2 \)[/tex].
