Question #d902d

1 Answer
Alan P.
Nov 18, 2016

#3x+y=14#

Explanation:

The line segment through the points #(2,3)# and #(5,4)#:

[1]#color(white)("XXX")#has a mid-point at #((2+5)/2,(3+4)/2)=(3.5,3.5)#

[2]#color(white)("XXX")#has a slope of #m=(Deltay)/(Deltax)=(4-3)/(5-2)=1/3#

The perpendicular bisector of this line segment:

[1]#color(white)("XXX")#passes through the midpoint #(3.5,3.5)#

[2]#color(white)("XXX")#has a slope of #-1/m=-3#

Using the slope-point form for the perpendicular
#color(white)("XXX")y-3.5=(-3)(x-3.5)#
or
#color(white)("XXX")3x+y=14#

Here is a picture to help verify the results:
enter image source here

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