How do I find the equation of a perpendicular bisector of a line segment with the endpoints #(-2, -4)# and #(6, 4)#?

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Jul 16, 2016

Answer:

#x+y-2 = 0#

Explanation:

Let #(x,y)# be any point on the perpendicular bisector. From elementary geometry, we can easily see that this point must be equidistant from the two points #(-2,-4) and (6,4)#. Using the Euclidean distance formula gives us the equation

#(x+2)^2 + (y+4)^2 = (x-6)^2 + (y-4)^2 #

This can be rewritten as

#(x+2)^2 - (x-6)^2 = (y-4)^2-(y+4)^2#

Using #a^2 -b^2 = (a+b)(a-b)#, this simplifies to

#8(2x-4) = -8*2y# which simplifies to

#x+y-2 = 0#

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