SOLUTION: What is the equation of the perpendicular bisector of the line between the points (2,2) and (6,6)?

Question 166434: What is the equation of the perpendicular bisector of the line between the points (2,2) and (6,6)?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
What is the equation of the perpendicular bisector of the line between the points (2,2) and (6,6)?
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ref:
http://www.purplemath.com/modules/midpoint.htm
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The midpoint between the points using the "mid-point formula" is
((x1+x2)/2, (y1+y2)/2)
((2+6)/2, (2+6)/2)
( 8/2, 8/2)
( 4, 4) (this is the mid-point)
.
Now, find the slope of the two points:
m=(y2-y1)/(x2-x1)
m=(6-2)/(6-2)
m=4/4
m=1 (this is the slope of the two points)
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The perpendicular bisector now has to have a "negative reciprocal" of 1 so our NEW line should have a slope of -1.
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So, our new line has:
slope = -1
crossing (4,4)
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y=mx + b
plugging in our info:
4=(-1)4 + b
4= -4 + b
8 = b
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Finally, we have:
m = -1
b = 8
so,
y = -x + 8 (THIS is what they're looking for)

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