What are corrdinates of the point equidistant from the points `(a,0,0),(0,a,0),(0,0,a) and (0,0,0)` ?

Options

A. `(a/3,a/3,a/3)`
B. `(a/2,a/2,a/2)`
C. (a,a,a)
D. `(2a,2a,2a)`

Answer

B

Explanation

let the point A(x, y, z) is equidistat from the point `B(a,0,0),C(0,a,0),D(0,0,a)and E(0,0,0)`.
Hence, `(x-a)^2+y^2+z^2=x^2+(y-a)^2+z^2`
`=x^2+y^2+(z-a)^2`
`=x^2+y^2=z^2`
`rArr (x-a)^2+y^2+z^2=x^2+(y-a)^2+z^2`
`rArr x^2+a^2-2ax+y^2+z^2=x^2+y^2+a^2-2ay+z^2`
`rArr ax=ayrArrx=y`
Similarly, `ay=azrArr y=z`
`rArr x=y=z`
`:. (x-a)^2+x^2+x^2=x^2+x^2+x^2`
`rArr x^2+a^2 -2ax+x^2+x^2=3x^2`
`rArr a^2=2axrArr x=a/2`
`:." Point is " (a/2, a/2,a/2)`