Determine the point on z-axis which is equidistant from the points (1, 5, 7) and (5, 1, -4)

Given: Points are A(1, 5, 7), B(5, 1, -4)


To find: the point on z-axis which is equidistant from the points


As we know x = 0 and y = 0 on z-axis


Let R(0, 0, z) any point on z-axis


According to the question:


RA = RB


RA2 = RB2


Formula used:


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



Therefore,


Distance between R(0, 0, z) and A(1, 5, 7) is RA,





Distance between R(0, 0, z) and B(5, 1, -4) is RB,





As RA2 = RB2


26+ (z – 7)2 = (z + 4)2 + 26


z2+ 49 – 14z + 26 = z2+ 16 + 8z + 26


49 – 14z = 16 + 8z


49 – 16 = 14z + 8z


22z = 33




Hence point on z-axis is equidistant from (1, 5, 7) and (5, 1, -4)


5