Question

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

Answer 1

Slope of perpendicular line: `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
`color(white)("XXX")(Deltay)/(Deltax)=-19/24`

Furthermore, if a line has a slope of `color(green)m` then any line perpendicular to it has a slope of `(-1/color(green)m)`

Therefore any line perpendicular to the line through the given points
must have a slope of `(-1/((-19/24)))=24/19`