What is the slope of any line perpendicular to the line passing through #(10,2)# and #(7,-2)#?

1 Answer
SagarStudy
Jan 23, 2016

#-3/4#

Explanation:

Let #m# be the slope of line passing through the given points and #m'# be the slope of line perpendicular to the line passing through the given points.

Since lines are perpendicular, therefore, the product of slopes will be equal to #-1#. i.e, #m*m'=-1#

#implies m'=-1/m#

#implies m'=-1/((y_2-y_1)/(x_2-x_1))#

#implies m'=-(x_2-x_1)/(y_2-y_1)#

Let #(7,-2)=(x_1,y_1)# and #(10,2)=(x_2,y_2)#

#implies m'=-(10-7)/(2-(-2))=-3/(2+2)=-3/4#

#implies m'=-3/4#

Hence, the slope of required line is #-3/4#.

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