What is the slope of any line perpendicular to the line passing through #(3,-2)# and #(12,19)#?

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Answer 1 · 2016-02-10T14:13:44

Slope of any line perpendicular to the line passing through #(3,−2)# and #(12,19)# is #-3/7#

If the two points are #(x_1, y_1)# and #(x_2, y_2)#, the slope of the line joining them is defined as

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

As the points are #(3, -2)# and #(12, 19)#

the slope of line joining them is #(19-(-2))/(12-3# or #21/9#

i.e. #7/3#

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

Hence slope of line perpendicular to the line passing through #(3,−2)# and #(12,19)# will be #-1/(7/3)# or #-3/7#.