Equivalence relation/Subset in R^n/Path connectedness/Exercise

Let ${}M\subseteq \mathbb {R} ^{n}$ be a subset with the induced metric. Consider the relation ${}R$ on ${}M$, where ${}xRy$ means that there exists a continuous mapping

$\gamma \colon [0,1]\longrightarrow M,t\longmapsto \gamma (t),$

with ${}\gamma (0)=x$ and ${}\gamma (1)=y$, Show that this is an equivalence relation on ${}M$.

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