Answer:
The slope of line r is [tex]\dfrac{ 4}{9}[/tex]
Step-by-step explanation:
Given as :
The points that line p contains is A ( - 1 , 4 ) and B ( 3 , - 5 )
Let The slope of line p = [tex]m_1[/tex]
So, [tex]m_1[/tex] = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Or , [tex]m_1[/tex] = [tex]\dfrac{ - 5 - 4}{3 - (- 1)}[/tex]
Or, [tex]m_1[/tex] = [tex]\dfrac{ - 9}{4}[/tex]
Now, Again ,
Line q is parallel to the line p
let The slope of line q = [tex]m_2[/tex]
So, for parallel lines
slope of lines are equal
I.e [tex]m_2[/tex] = [tex]m_1[/tex]
∴ [tex]m_2[/tex] = [tex]\dfrac{ - 9}{4}[/tex]
Again ,
Line r is perpendicular to the line q
let The slope of line r = [tex]m_3[/tex]
So, for perpendicular lines
The product of the slopes of two line = - 1
[tex]m_3[/tex] × [tex]m_2[/tex] = - 1
or, [tex]m_3[/tex] × [tex]\dfrac{ - 9}{4}[/tex] = - 1
or, [tex]m_3[/tex] = [tex]\frac{-1}{\frac{-9}{4}}[/tex]
∴ [tex]m_3[/tex] = [tex]\dfrac{ 4}{9}[/tex]
So, The slope of line r = [tex]m_3[/tex] = [tex]\dfrac{ 4}{9}[/tex]
Hence , The slope of line r is [tex]\dfrac{ 4}{9}[/tex] . Answer
