SOLUTION: Three points have coordinates A(2,9) B(9,7) and C(2,0). Find a) the equation of the perpendicular bisector of AB, b) the equation of the perpendicular bisector of BC, c) the poi

Algebra ->  Triangles -> SOLUTION: Three points have coordinates A(2,9) B(9,7) and C(2,0). Find a) the equation of the perpendicular bisector of AB, b) the equation of the perpendicular bisector of BC, c) the poi      Log On


   

Question 1177470: Three points have coordinates A(2,9) B(9,7) and C(2,0). Find
a) the equation of the perpendicular bisector of AB,
b) the equation of the perpendicular bisector of BC,
c) the point of intersection of the two perpendicular bisectors.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
AB has a midpoint of (5.5, 8)
the slope of AB is -2/7
the equation of the line is y-y1=m(x-x1) m slope (x1, y1) point
this is at y-9=(-2/7)(x-2)
y=(-2/7)x+67/7
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the perpendicular bisector of this line has slope 7/2 and the point is (11/2, 8)
y-8=(7/2)(x-11/2)
y=(7/2)x-45/4
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BC has a midpoint of (5.5, 3.5)
slope is 1
equation is y=x-2
perpendicular bisector has slope -1 and its equation of y-3.5=-1(x-5.5)
y=-x+9
first graph are lines AB and BC
graph%28300%2C300%2C-10%2C12%2C-10%2C12%2C-%282%2F7%29x%2B67%2F7%2Cx-2%29
second is perpendicular bisector of AB
graph%28300%2C300%2C-10%2C12%2C-10%2C12%2C%287%2F2%29x-45%2F4%2C%28-2x%2F7%29%2B67%2F7%29
third is perpendicular bisector of BC
graph%28300%2C300%2C-10%2C12%2C-10%2C12%2Cx-2%2C-x%2B9%29
last is graph of the perpendicular bisectors
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%287%2F2%29x-45%2F4%2C-x%2B9%29
equation of perpendicular bisector of AB is y=(7/2)x-45/4
of BC it is y=-x+9