Moving Paths with Space, but what if ?

You can use the direct selection tool of the group selection tool (both tools are the lowercase a {hold shift to select the other}) Clicking the path will let you move the entire path. The direct selection tool lets you move just the point whereas the group selection tool selects the entire path. With the direct selection tool you can also drag select the points. They will only move when the cursor is over a point.

Play with them a bit.