Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine which line is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the perpendicular line. The key is understanding the relationship between the slopes of perpendicular lines.
The slopes of two perpendicular lines are negative reciprocals of each other. This means if one line has a slope [tex]\( m \)[/tex], the perpendicular line's slope will be [tex]\( -\frac{1}{m} \)[/tex].
Given:
1. The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
To find the slope of the line perpendicular to this:
1. Take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
The negative reciprocal formula states:
[tex]\[ \text{slope of the perpendicular line} = -\left(\frac{1}{-\frac{5}{6}}\right) \][/tex]
Simplifying this:
[tex]\[ -\left(\frac{1}{-\frac{5}{6}}\right) = -\left(-\frac{6}{5}\right) = \frac{6}{5} \][/tex]
So, the slope of the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Thus, whichever of the lines JK, LM, NO, or PQ that has a slope of [tex]\(\frac{6}{5}\)[/tex] would be the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
In conclusion, the line perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of [tex]\(\frac{6}{5}\)[/tex].
The slopes of two perpendicular lines are negative reciprocals of each other. This means if one line has a slope [tex]\( m \)[/tex], the perpendicular line's slope will be [tex]\( -\frac{1}{m} \)[/tex].
Given:
1. The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
To find the slope of the line perpendicular to this:
1. Take the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex].
The negative reciprocal formula states:
[tex]\[ \text{slope of the perpendicular line} = -\left(\frac{1}{-\frac{5}{6}}\right) \][/tex]
Simplifying this:
[tex]\[ -\left(\frac{1}{-\frac{5}{6}}\right) = -\left(-\frac{6}{5}\right) = \frac{6}{5} \][/tex]
So, the slope of the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Thus, whichever of the lines JK, LM, NO, or PQ that has a slope of [tex]\(\frac{6}{5}\)[/tex] would be the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
In conclusion, the line perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of [tex]\(\frac{6}{5}\)[/tex].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.