Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine which line is perpendicular to a line that has a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to figure out the slope of the perpendicular line.
For two lines to be perpendicular, the product of their slopes must be [tex]\(-1\)[/tex]. So, if the slope of the original line is [tex]\( m_1 = -\frac{5}{6} \)[/tex], the slope [tex]\( m_2 \)[/tex] of the perpendicular line can be calculated using the relationship:
[tex]\[ m_1 \times m_2 = -1 \][/tex]
Given the slope of the original line [tex]\( m_1 = -\frac{5}{6} \)[/tex], we substitute this into the equation:
[tex]\[ -\frac{5}{6} \times m_2 = -1 \][/tex]
To solve for [tex]\( m_2 \)[/tex], we rearrange the equation:
[tex]\[ m_2 = \frac{-1}{-\frac{5}{6}} \][/tex]
When we simplify [tex]\(\frac{-1}{-\frac{5}{6}}\)[/tex], we get:
[tex]\[ m_2 = \frac{6}{5} = 1.2 \][/tex]
So, the slope of the perpendicular line is [tex]\( 1.2 \)[/tex].
Thus, any line with a slope of [tex]\( 1.2 \)[/tex] will be perpendicular to a line with a slope of [tex]\( -\frac{5}{6} \)[/tex]. To identify which specific line (JK, LM, NO, PQ) corresponds to this slope, further information about the slopes of these lines would be required, which is not provided in the question. Therefore, we conclude that the perpendicular line to the given slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of [tex]\(1.2\)[/tex].
For two lines to be perpendicular, the product of their slopes must be [tex]\(-1\)[/tex]. So, if the slope of the original line is [tex]\( m_1 = -\frac{5}{6} \)[/tex], the slope [tex]\( m_2 \)[/tex] of the perpendicular line can be calculated using the relationship:
[tex]\[ m_1 \times m_2 = -1 \][/tex]
Given the slope of the original line [tex]\( m_1 = -\frac{5}{6} \)[/tex], we substitute this into the equation:
[tex]\[ -\frac{5}{6} \times m_2 = -1 \][/tex]
To solve for [tex]\( m_2 \)[/tex], we rearrange the equation:
[tex]\[ m_2 = \frac{-1}{-\frac{5}{6}} \][/tex]
When we simplify [tex]\(\frac{-1}{-\frac{5}{6}}\)[/tex], we get:
[tex]\[ m_2 = \frac{6}{5} = 1.2 \][/tex]
So, the slope of the perpendicular line is [tex]\( 1.2 \)[/tex].
Thus, any line with a slope of [tex]\( 1.2 \)[/tex] will be perpendicular to a line with a slope of [tex]\( -\frac{5}{6} \)[/tex]. To identify which specific line (JK, LM, NO, PQ) corresponds to this slope, further information about the slopes of these lines would be required, which is not provided in the question. Therefore, we conclude that the perpendicular line to the given slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of [tex]\(1.2\)[/tex].
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.