To determine which line is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], follow these steps:
1. Understand the Relationship:
- For two lines to be perpendicular, the product of their slopes must equal [tex]\(-1\)[/tex].
2. Find the Perpendicular Slope:
- Let the slope of the given line be denoted as [tex]\( m_1 = -\frac{5}{6} \)[/tex].
- If [tex]\( m_2 \)[/tex] is the slope of the line that is perpendicular to the given line, then:
[tex]\[ m_1 \times m_2 = -1 \][/tex]
Substituting the given slope into the equation, we get:
[tex]\[ -\frac{5}{6} \times m_2 = -1 \][/tex]
3. Solve for [tex]\( m_2 \)[/tex]:
- To find [tex]\( m_2 \)[/tex], we can isolate [tex]\( m_2 \)[/tex] by dividing both sides of the equation by [tex]\(-\frac{5}{6}\)[/tex]:
[tex]\[ m_2 = \frac{-1}{-\frac{5}{6}} \][/tex]
4. Simplify the Expression:
- When simplifying the division of fractions, we can multiply by the reciprocal of the denominator:
[tex]\[ m_2 = -1 \div -\frac{5}{6} = -1 \times -\frac{6}{5} = \frac{6}{5} \][/tex]
5. Express the Result as a Decimal:
- Convert [tex]\(\frac{6}{5}\)[/tex] to a decimal to make it easier to interpret:
[tex]\[ \frac{6}{5} = 1.2 \][/tex]
Therefore, the slope of any line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(1.2\)[/tex].
To know which specific line (JK, LM, NO, PQ) corresponds to this perpendicular slope, we would need additional information about the slopes of these lines. However, based on the provided numerical solution, the correct answer aligns with determining that the slope of the perpendicular line is [tex]\(1.2\)[/tex].
