Answer :

The general point on xy plane is D(x, y, 0). Consider this point is equidistant to the points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1).


AD = BD



Squaring both sides,


=


X2 – 4x +4 + y2 + 9 = X2 + y2 -6y + 9 + 4


-4x = -6y ….(1)


Also, AD = CD



Squaring both sides,


=


X2 – 4x +4 + y2 + 9 = X2 + y2 +1


-4x = -12 ….(2)


Simultaneously solving equation (1) and (2) we get


X = 3, y = 2.


The point which is equidistant to the points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1) is (3, 2, 0).


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