Question 995717: two schools are located at points P (-1,4) Q (7, -2) on a town map. the school board is planning a new sports complex to be used by both schools. the board wants to find a location equidistant from the 2 schools. Use an equation to represent the possible locations for the sports complex?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! two schools are located at points P (-1,4) Q (7, -2) on a town map. the school board is planning a new sports complex to be used by both schools. the board wants to find a location equidistant from the 2 schools. Use an equation to represent the possible locations for the sports complex?
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Comment:: Find the equation of the perpendicular bisector (PB) of line PQ.
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slope of PQ = (-2-4)/(7--1) = -6/8 = -3/4
slope of perpendicular bisector: 4/3
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mid-point of PQ:: [(-1+7)/2 , (4-2)/2] = (3,1)
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Form of PB :: y = mx + b
Solve for "b"::
1 = (4/3)3+b
b = -3
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Ans: y = (4/3)x - 3
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Cheers,
Stan H.
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