I don't know how TFS handles this, but I do know TFS is a fork of an old Perforce release.

Perforce has a command "p4 where". If you provide it a depot path, or a local file system path, it will return the depot path, local file system path, and local workspace mapping path.

This information was all held server side. It's possible this is true for how TFS handles it too based on it's legacy of being an old Perforce derivative.

Looking at the TFS command list, "tf properties" looks to provide some options that may work like p4 where.
https://msdn.microsoft.com/en-us/library/tzy14b58(v=vs.100).aspx