What is the slope of any line perpendicular to the line passing through #(-21,2)# and #(-32,5)#?

1 Answer
iceman
Dec 16, 2015

slope of the perpendicular line #=11/3#

Explanation:

First we need to find the slope of the line passing through the points: #(-21, 2) and (-32, 5)#, the slope #m# between the points:
#(x_1, y_1) and (x_2, y_2)# is given by:
#m=(y_2-y_1)/(x_2-x_1)#, so in this case:
#m=(5-2)/(-32-(-21))#, simplifying we get:
#m=3/(-32+21)=3/-11=-3/11#
Now the perpendicular lines have slopes that are negative reciprocals, so if #m_1 and m_2# are the slopes of the two perpendicular lines then:
#m_2=-1/m_1#, therefore in this case:
#m_2= -1/(-3/11) = 11/3#

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