Can you explain again how to determine distance by using Cepheids?
See question above for the properties of Cepheids. The idea behind using them to measure distances is that you can determine the intrinsic luminosity of a Cepheid by measuring its period! If you know the intrinsic luminosity, and you measure the apparent brightness, you can find the approximate distance to a Cepheid (and to a Cepheid-containing galaxy). This technique works pretty well out to a few tens of millions of light-years.