SOLUTION: find the equation of the perpendicular bisect of AB given that A is (2,7) and B is (6,-1).

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Question 1127763: find the equation of the perpendicular bisect of AB given that A is (2,7) and B is (6,-1).
Answer by MathLover1(20855) About Me  (Show Source):
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find the equation of the perpendicular bisect of AB given that A+ is (2,7) and B is (6,-1).
first find equation of a line passing through points
A+ (2,7) and B (6,-1)
y=mx%2Bb where m is a slope and b is y-intercept
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%28-1-7%29%2F%286-2%29
m=-8%2F4
m=-2
y=-2x%2Bb ....plug in (2,7)
7=-2%2A2%2Bb
7=-4%2Bb
7%2B4=b
b=11
so, y=-2x%2B11
recall that the perpendicular line will have a slope negative reciprocal to a slope of this line
so, -1%2Fm=-1%2F-2=1%2F2
y=%281%2F2%29x%2Bb
the perpendicular bisect of AB, we can find coordinates o midpoint of AB
A+ (2,7) and B (6,-1)
(%282%2B6%29%2F2,%287-1%29%2F2)
=>(4,3)
-> the perpendicular bisect is passing through (4,3), use it to find y-intercept b
3=%281%2F2%294%2Bb
3=2%2Bb
3-2=b
b=1
and equation is: y=%281%2F2%29x%2B1