What is the slope of any line perpendicular to the line passing through #(8,12)# and #(5,-2)#?

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Answer 1 · 2016-02-16T17:20:27

The slope #=-3/14#

Consider the points :
#(x_1, y_1) = color(blue)((8,12)#
#(x_2, y_2) = color(blue)((5,-2)#

The slope joining the pair of points is calculated as :

#(y_2-y_1)/(x_2-x_1)#

#= (-2-12)/(5-8)#

#= (-14)/(-3)#

#= 14/3#

The product of slopes of two lines perpendicular to each other is #-1#.

Hence slope of line perpendicular to the line passing through #(8,12)# and #(5,-2)# will be #-1/(14/3)# or #-3/14#.