Let $\sim$ be the relation on $\mathbb R^2$ defined by: $$(x_1, y_1) ∼ (x_2, y_2) \iff x_1^2 + y_1^2=x_2^2+y_2^2$$ Show that $\sim$ is an equivalence relation on $\mathbb R^2$.
Consider the function $f \colon [0, \infty) \to \mathbb R^2/ \sim$ defined by $f(x) = [(x, 0)]$ $\forall x \in [0, \infty)$. Show that $f$ is bijective.
I have shown it is an equivalence relation and that $f$ is injective but I am now stuck on proving it is surjective. I really am not sure how to begin because it seems obvious it is true? Any hints appreciated