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,


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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