What is the slope of any line perpendicular to the line passing through #(-3,-12)# and #(5,-3)#?

1 Answer
mason m
Dec 12, 2015

#-8/9#

Explanation:

A line perpendicular to another line has an OPPOSITE RECIPROCAL slope.

For example, if a line had a slope of #2#, the perpendicular line's slope would be #-1/2#.
Similarly, a line with slope #-3/5# would be perpendicularly intersected by a line with a slope of #5/3#.

To find the slope of the perpendicular line, first find the slope of the original line.

#"slope"=(y_2-y_1)/(x_2-x_1)#

#=(-3-(-12))/(5-(-3))=(-3+12)/(5+3)=9/8#

The perpendicular line's slope will be the opposite reciprocal of #9/8#, which is #-8/9#.

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