Question

Line p contains points A(-1,4) and B(3,-5) lines q is parallel to line p. Line r is perpendicular to Line q. What is the slip of line r

Answer 1

Answer:

The slope of line r is $\dfrac{ 4}{9}$

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 = $m_1$

So,  $m_1$ = $\dfrac{y_2-y_1}{x_2-x_1}$

Or , $m_1$ = $\dfrac{ - 5 - 4}{3 - (- 1)}$

Or, $m_1$ = $\dfrac{ - 9}{4}$

Now, Again ,

Line q is parallel to the line p

let The slope of line q  =  $m_2$

So, for parallel lines

slope of lines are equal

I.e  $m_2$ = $m_1$

∴  $m_2$ = $\dfrac{ - 9}{4}$

Again ,

Line r is perpendicular to the line q

let The slope of line r  =  $m_3$

So, for perpendicular lines

The product of the slopes of two line = - 1

$m_3$ × $m_2$ = - 1

or, $m_3$ ×  $\dfrac{ - 9}{4}$  = - 1

or,  $m_3$  = $\frac{-1}{\frac{-9}{4}}$

∴  $m_3$ =  $\dfrac{ 4}{9}$

So, The slope of line r =  $m_3$ =  $\dfrac{ 4}{9}$

Hence , The slope of line r is $\dfrac{ 4}{9}$  . Answer