Does there exist a $G$-invariant polynomial $f \in \mathbb{C}[x_1, \ldots, x_n]^G$ such that $f(u_1, \ldots, u_n) = 0$ and $f(v_1, \ldots, v_n) = 1$?

Question

Let $G$ be a finite subgroup of $\text{GL}(\mathbb{C}^n)$ and let $u = (u_1, \ldots, u_n)$, $v = (v_1, \ldots, v_n) \in \mathbb{C}^n$ be two points which do not belong to the same $G$-orbit in $\mathbb{C}^n$.

Question. Does there exist a $G$-invariant polynomial $f \in \mathbb{C}[x_1, \ldots, x_n]^G$ such that $f(u_1, \ldots, u_n) = 0$ and $f(v_1, \ldots, v_n) = 1$?