What is the slope of any line perpendicular to the line passing through #(2,7)# and #(5,2)#?

1 Answer
Prof_S
Jan 9, 2016

The line has slope #(2-7)/(5-2)# or -#5/3#, so the slope of a perpendicular line is #3/5#

Explanation:

The slope of a line is the "rise" over the "run". That is, the change in the elevation divided by the distance between the measurements of elevation. In this example, by going from x=2 to x=5, a distance of 3, the elevation falls from 7 to 2, a change of -5. So, the slope of the line is #-5/3#. The slope of a line perpendicular is obtained by inverting the given slope and changing the sign, so #3/5#

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