What is the slope of any line perpendicular to the line passing through #(2,2)# and #(3,-5)#?

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Answer 1 · 2018-03-12T19:23:10

#1/7#

Denoting

#(2, 2)# by #(x_1, y_1)#

and

#(3, -5)# by #(x_2, y_2)#

The slope of the line is the rise (difference between #y# values) divided by the run (difference between #x# values).

Denoting the slope by #m#

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

#= (-5 - 2)/(3 - 2)#

#= -7/1#

that is

#m = -7#

The slope of a line perpendicular to some other line is the negative reciprocal.

Denoting the required slope by #m'#

#m' = -1/m = - 1/(-7) = 1/7#