A specific quotient homeomorphic to $S^{n-1}$

Question

Let $\Gamma=\mathbb{R}_{>0}$ be the group of strictly positive reals, endowed with the usual multiplication. Let $X=\mathbb{R}^n\setminus \{0\}$. I already showed that $$ \Gamma \times X \rightarrow X, (r,x)\mapsto rx$$ (the usual multiplication of vectors $x$ by scalars $r$) defines an action of $\Gamma$ on $X$. Now i have to prove that $X/ \Gamma$ is homeomorphic to $S^{n-1}$. I have no clue why this is true, so I don't even know how to start. Can somebody help me?