Answer :

Given: Points are O(0, 0, 0), A(a, 0, 0), B(0, b, 0) and C(0, 0, c)


To find: the coordinates of point which is equidistant from the points


Let required point P(x, y, z)


According to question:


PA = PB = PC = PO


PA2 = PB2 = PC2 = PO2


Formula used:


Distance between any two points (a, b, c) and (m, n, o) is given by,



Therefore,


The distance between P(x, y, z) and O(0, 0, 0) is PO,




Distance between P(x, y, z) and A(a, 0, 0) is PA,




Distance between P(x, y, z) and B(0, b, 0) is PB,




Distance between P(x, y, z) and C(0, 0, c) is PC,




As PO2 = PA2


x2+ y2 + z2 = (x – a)2 + y2 + z2


x2= x2+ a2 – 2ax


2ax = a2



As PO2 = PB2


x2+ y2 + z2 = x2+ (y – b)2 + z2


y2= y2+ b2 – 2by


2by = b2



As PO2 = PC2


x2+ y2 + z2 = x2 + y2 + (z – c)2


z2= z2+ c2 – 2cz


2cz = c2



Hence point is equidistant from given points


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