Question

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

Answer 1

Answer:

The slope of the line perpendicular to the line segment having slope $-\dfrac{3}{4}$ is $\dfrac{4}{3}$

Step-by-step explanation:

Given the slope of the line perpendicular to the line segment is $-\dfrac{3}{4}$

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

$m_{2} =-\frac{1}{m_{1} }$

$m_{2} =-\frac{1}{-\frac{3}{4} }$

$m_{2} =\dfrac{4}{3}$

Answer 2

Answer:

The slope of line perpendicular to the line segment that has a slope of $\dfrac{-3}{4}$ is $\dfrac{4}{3}$

Step-by-step explanation:

Given,

The line segment has a slope of $\dfrac{-3}{4}$.

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,

$\begin{aligned}\dfrac{-3}{4}\times{\rm{slope\;of\;perpendicular\;line}}&=-1\\{\rm{slope\;of\;perpendicular\;line}}&=\dfrac{4}{3}\end{aligned}$