The Mazur-Ulam Theorem Theorem $2.1$ states that any surjective isometry between any two real normed spaces $f:X \rightarrow Y$ is affine.
In the proof of the theorem, the author mentioned that it suffices to show that for any $x, y \in X$, $$f\left(\dfrac{x+y}{2}\right) = \dfrac{f(x)+f(y)}{2}$$
Why is it the case? How to conclude $f$ is affine from equation above?
Recall that $f:X \rightarrow Y$ is an affine function if for all $x,y \in X$ and $0 \leq t \leq 1$, $$f[(1-t)x+ty] = (1-t)f(x) + t f(y)$$