What is the equation of the line that passes through #(2,1)# and is perpendicular to the line that passes through the following points: #(8,-5),(3,9) #?

1 Answer
SagarStudy
Jan 10, 2016

Let #A=(2,1), B=(8,-5), C=(3,9)#

First of all we have to find out the slope of the line that passes through #B# and #C#.
After knowing the slope of the line passing through #B# and #C# we can find the slope of the line that is perpendicular to #BC#.

Slope of #BC=(9-(-5))/(3-8)=(9+5)/-5=12/-5=-12/5=m#

Let the slope of the line perpendicular to #BC# be #m'#.
Then #m.m'=-1#

#implies m'=-1/m=-1/(-12/5)=5/12#

#implies m'=5/12#

Now, we know two things about the required line
(i) Slope of that line #m'=5/12#

(ii) The point through which the line passes #(2,1)#.

These two things are enough to find the equation.

Using point-slope form

#y-y_1=m'(x-x_1)#

#implies y-1=5/12(x-2)#

#implies 12y-12=5x-10#
#implies 5x-12y+2=0#

This is the required equation.

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