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Question

Find the coordinates of the point equidistant from three given points A(5,3),B(5,5) and C(1,5).

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Solution

Let the coordintaes of the point be O(x,y), then
OA=OB=OC
or OA2=OB2=OC2
OA2=(5x)2+(3y)2
OB2=(5x)2+(5y)2
OC2=(1x)2+(5y)2
(5x)2+(3y)2=(5x)2+(5y)2
96y+y2=25+10y+y2
925=10y+6y
16y=16
y=1616=1
and (5x)2+(5y)2
=(1x)2+(5y)2
2510x+x2=12x+x2
10x+2x=125
8x=24
or x=3
So, coordinates of the point is (3,1).

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