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

1 Answer
Alan P.
Oct 16, 2017

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#

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