What is the slope of any line perpendicular to the line passing through #(-20,32)# and #(1,5)#?

1 Answer
sente
Dec 31, 2015

#7/9#

Explanation:

Given two lines with slopes #m_1# and #m_2#, we say the lines are perpendicular if #m_1m_2 = -1#. Note that this implies #m_2= -1/m_1#.

Then, to find the slope #m_2# of a line perpendicular to the line passing through #(-20, 32)# and #(1, 5)# all we need to do is find the slope #m_1# of the given line and apply the above formula.

The slope of a line passing through points #(x_1,y_1)# and #(x_2,y_2)# is given by #"slope" = "increase in y"/"increase in x" = (y_2-y_1)/(x_2-x_1)#

So
#m_1 = (5-32)/(1-(-20)) = (-27)/21 = -9/7#

Applying #m_2 = -1/m_1# this means the slope #m_2# of a line perpendicular to that line will be

#m_2 = -1/(-9/7) = 7/9#

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