Configurations of points on a line up to scaling or translation

We prove that the Losev--Manin compactification of the space of configurations of $n$ points on ${\mathbb P}^1 \backslash \{0,\infty\}$ modulo scaling degenerates (isotrivially) to a compactification of the space of configurations of $n$ points on ${\mathbb A}^1$ modulo translation. The latter resembles the compactification constructed by Ziltener and Mau--Woodward, but allows the marked points to coincide, making it a ${\mathbb G}_a^{n-1}$-variety, which mirrors the fact that the Losev--Manin space is toric. The degeneration is compatible with the actions of ${\mathbb G}_m^{n-1}$ and ${\mathbb G}_a^{n-1}$ in the sense that these actions fit together globally in the total space of the degeneration.