# What is the slope of any line perpendicular to the line passing through (30,39) and (54,20)?

Oct 16, 2017

Slope of perpendicular line: $\frac{24}{19}$

#### Explanation:

For the given points, we have
color(white)("XXX"){: (ul(x),color(white)("xxx"),ul(y)), (30,,39),(54,,20), (color(white)("XX"),,color(white)("XX")), (ul(Deltax),,ul(Deltay)), (-24,,19) :}

By definition the slope of the line connecting these point is
$\textcolor{w h i t e}{\text{XXX}} \frac{\Delta y}{\Delta x} = - \frac{19}{24}$

Furthermore, if a line has a slope of $\textcolor{g r e e n}{m}$ then any line perpendicular to it has a slope of $\left(- \frac{1}{\textcolor{g r e e n}{m}}\right)$

Therefore any line perpendicular to the line through the given points
must have a slope of $\left(- \frac{1}{\left(- \frac{19}{24}\right)}\right) = \frac{24}{19}$