8. (i) (Grade 11) In an isosceles right triangle, the right-angle vertex $A(1,0)$, and the centroid $G(2,0)$. Then the coordinates of the other two vertices $B$ and $C$ are $\qquad$
(ii) (Grade 12) The area of the orthogonal projection of a regular tetrahedron with edge length 1 on a horizontal plane is $S$. Then the maximum value of $S$ is $\qquad$
8. (i) $\left(\frac{5}{2}, \frac{3}{2}\right)$ and $\left(\frac{5}{2},-\frac{3}{2}\right)$.
Let the midpoint of the hypotenuse be $D$.
From $|A G|=2|G D|$, we get $D\left(\frac{5}{2}, 0\right)$.
Let the other two vertices be $B$ and $C$, then $B D$ is perpendicular and equal to $A D$.
Thus, we get $B\left(\frac{5}{2}, \frac{3}{2}\right)$ and $C\left(\frac{5}{2},-\frac{3}{2}\right)$.
(ii) $\frac{1}{2}$.
The projection can only be a triangle or a quadrilateral, and the length of the projected line segment is no greater than the original line segment. When the projection is a triangle, $s \leqslant \frac{\sqrt{3}}{4}$; when the projection is a quadrilateral, the diagonal length is less than or equal to 1, then $S \leqslant$ $\frac{1}{2}$, and $\frac{1}{2}$ can be achieved (when the diagonals are perpendicular to each other).