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Determine the point in XY - plane which is equidistant from three points A(2,0,3) B(0,3,2) and C(0,0,1).

Asked by Topperlearning User 13th November 2016, 9:52 PM
Answered by Expert
Answer:

L e t space t h e space p o i n t space P equals left parenthesis x comma y comma 0 right parenthesis
A c c o r d i n g space t o space t h e space q u e s t i o n
P A equals P B
rightwards double arrow P A squared equals P B squared
rightwards double arrow left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 0 right parenthesis squared plus left parenthesis 0 minus 3 right parenthesis squared equals left parenthesis x minus 0 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared plus left parenthesis 0 minus 2 right parenthesis squared
rightwards double arrow negative 4 x plus 13 equals negative 6 y plus 13
rightwards double arrow 2 x equals 3 y
P B equals P C
rightwards double arrow P B squared equals P C squared
rightwards double arrow left parenthesis x minus 0 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared plus left parenthesis 0 minus 2 right parenthesis squared equals left parenthesis x minus 0 right parenthesis squared plus left parenthesis y minus 0 right parenthesis squared plus left parenthesis 0 minus 1 right parenthesis squared
rightwards double arrow negative 6 y plus 13 equals 1
rightwards double arrow y equals 2
2 x equals 3 y rightwards double arrow x equals 3
S o space t h e space c o minus o r d i n a t e s space o f space P space equals left parenthesis 3 comma 2 comma 0 right parenthesis

Answered by Expert 13th November 2016, 11:52 PM
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