1. Prove that the most general transformation which leaves the origin fixed and preseerves all distances is either a rotation or a rotation followd by reflexion in the real axis.
2. Show that any four distinct points can be carried by a linear transformation to position 1, -1, k, -k, where the value of k depends on the points. How many solutions are there, and how are they related?
Please help me to solve these problems. Thanks!