Question

A line segment has a slope of -3/4. What is the slope of a line perpendicular to this line segment

Answer 1

The slope of line perpendicular to the line segment that has a slope of
`(-3)/(4)` is
`(4)/(3)`

Explanation:

Given,

The line segment has a slope of
`(-3)/(4)`.

To find:

The slope of the line that is perpendicular to the given line segment.

Now,

Let suppose a line
`L_1` has a slope
`m_1` and line
`L_2` has a slope
`m_2`.

Condition for perpendicularity:

If the product of the slopes of these lines equals -1, then the lines are perpendicular to each other.

Therefore, apply the above condition to our question.

So,

`\begin{aligned}(-3)/(4)*{\rm{slope\;of\;perpendicular\;line}}&=-1\\{\rm{slope\;of\;perpendicular\;line}}&=(4)/(3)\end{aligned}`

Answer 2

The slope of the line perpendicular to the line segment having slope
`-(3)/(4)` is
`(4)/(3)`

Explanation:

Given the slope of the line perpendicular to the line segment is
`-(3)/(4)`

The expressions for the slope of line which are perpendicular to each other is given as
`m_(1) m_(2) =-1`

So the slope of the perpendicular line will be

`m_(2) =-(1)/(m_(1) )`

`m_(2) =-(1)/(-(3)/(4) )`

`m_(2) =(4)/(3)`