If we have $P_1,...,P_n$, and $Q_1,...,Q_n$ points in an euclidian space such that $ d(P_i,P_j) = d(Q_i,Q_j)$, its easy to show that using up to $n$ reflections, we can map each $P_i$ into $Q_i$. The proof is constructive. We use the reflection $R_i$ to send $P_i$ into $Q_i$ and show that all the previous points ($P_1, ..., P_{i-1}$) stay fixed. I have two questions about this method:
-Does the order of the points affect the total number of reflections?
-Does this method uses the least amount of reflections required?