To determine which line is perpendicular to a given line, we need to understand the relationship between their slopes. Specifically, if two lines are perpendicular, the product of their slopes will be \(-1\).
Given the slope of the original line as \( -\frac{5}{6} \), we need to find the slope of the perpendicular line. Let the slope of this perpendicular line be \( m \).
We know the following relationship:
[tex]\[ \text{slope of original line} \times \text{slope of perpendicular line} = -1 \][/tex]
Substitute the given slope of the original line:
[tex]\[ -\frac{5}{6} \times m = -1 \][/tex]
To find \( m \), solve the equation:
[tex]\[ m = \frac{-1}{-\frac{5}{6}} \][/tex]
When dividing by a fraction, we multiply by its reciprocal:
[tex]\[ m = -1 \times -\frac{6}{5} \][/tex]
Simplify the expression:
[tex]\[ m = \frac{6}{5} \][/tex]
Therefore, the slope of the line that is perpendicular to the original line with a slope of \( -\frac{5}{6} \) is \( \frac{6}{5} \).
Since the exact lines (JK, LM, NO, PQ) given in the options do not have specified slopes, any of these lines could theoretically have the slope [tex]\( \frac{6}{5} \)[/tex]. To determine the specific line that is perpendicular, you would need additional information about the slopes of the given lines.
