The Move Through Center tool is very similar to the Move tool except that it moves the path along a vector starting at the center of the path and defined by a second using the Mark Button
You can achieve the same effect using the Move tool, but you’ll need to know where the center of the path is, select it, and then use the move-by-vector construction option. The Move Through Center tool is a convenience tool that simplifies this process. Here’s an example.
There is one other construction option that can be set before construction begins. On the Transformations tab there's a checkbox labeled "Create Copy"
If this is enabled, a copy of the path will be created. The original path will not be affect in any way.