To determine which line is perpendicular to a given line with a slope of \( -\frac{5}{6} \), we need to recall an important property of perpendicular lines: the slopes of two perpendicular lines are negative reciprocals of each other.
Here's the step-by-step solution:
1. Identify the given slope: The given slope of the line is \( -\frac{5}{6} \).
2. Find the negative reciprocal of the given slope:
- The negative reciprocal of a number \( a \) is found by taking the reciprocal of \( a \) (which means swapping the numerator and denominator) and then changing its sign.
- The reciprocal of \( -\frac{5}{6} \) is \( -\frac{6}{5} \).
- Changing the sign of \( -\frac{6}{5} \) gives \( \frac{6}{5} \).
3. Converting the slope to decimal form:
- \( \frac{6}{5} \) as a decimal is \( 1.2 \).
Therefore, a line that is perpendicular to a line with a slope of \( -\frac{5}{6} \) has a slope of \( 1.2 \).
To determine which specific line (line JK, line LM, line NO, or line PQ) is perpendicular, we would need to know the slopes of those lines. However, based on the information given, we have established that the slope of the perpendicular line should be \( 1.2 \).
Identify the line among JK, LM, NO, and PQ whose slope matches [tex]\( 1.2 \)[/tex] and that will be our answer.
