Statement-I : The coordinates of a point equidistant from the four points $\left(\mathrm{a},0,0\right),\left(0,\mathrm{b},0\right),\left(0,0,\mathrm{c}\right),\left(0,0,0\right)$ are $\left(\frac{\mathrm{a}}{4},\frac{\mathrm{b}}{4},\frac{\mathrm{c}}{4}\right)$

Statement-II : The distance between the origin and the centroid of the tetrahedron where vertices are $\left(0,0,0\right),\left(\mathrm{a},0,0\right),\left(0,\mathrm{b},0\right),\left(0,0,\mathrm{c}\right)$ is $\frac{\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2}}{4}$

Which of the above statements is correct :

The given points are $\left(a,0,0\right),\left(0,b,0\right),\left(0,0,c\right)$ and $\left(0,0,0\right)$

The distances from $\left(\frac{a}{4},\frac{b}{4},\frac{c}{4}\right)$ to the above points are $\sqrt{\frac{15a^2}{16}+\frac{b^2}{16}+\frac{c^2}{16}}$,$\sqrt{\frac{a^2}{16}+\frac{15b^2}{16}+\frac{c^2}{16}}$ and so on

observing the above distances, any two distances are not equal

hence the statement I is not true

$\left(\frac{a}{4},\frac{b}{4},\frac{c}{4}\right)$ is centroid of the tetrahedron formed by the given four vertices, and the distance of it from origin is $\sqrt{\frac{a^2}{4}+\frac{b^2}{4}+\frac{c^2}{4}}$

Hence, the statement II is true.