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

The slope of line r is
`( 4)/(9)`

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` =
`(y_2-y_1)/(x_2-x_1)`

Or ,
`m_1` =
`( - 5 - 4)/(3 - (- 1))`

Or,
`m_1` =
`( - 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` =
`( - 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` ×
`( - 9)/(4)` = - 1

or,
`m_3` =
`(-1)/((-9)/(4))`

∴
`m_3` =
`( 4)/(9)`

So, The slope of line r =
`m_3` =
`( 4)/(9)`

Hence , The slope of line r is
`( 4)/(9)` . Answer