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How would I use MAC address to locate router
Assuming you mean the MAC address of the router (the MAC address of any other machine won't help):
If you have a machine on the same LAN segment as the router, using the router to communicate with other machines, and it's running some flavor of UN*X or Windows and you have access to its command line, try running the command arp -a. That will print the machine's ARP table, which may have an entry of the form
XXX (AAA.BBB.CCC.DDD) at XX:YY:ZZ:UU:VV:WW ...
which says that the MAC address for the IP address AAA.BBB.CCC.DDD is XX:YY:ZZ:UU:VV:WW; if the MAC address you have for the router is XX:YY:ZZ:UU:VV:WW, you now know one of the IP addresses of the router, in addition to the MAC address you already knew.
In addition, the XX:YY:ZZ part might help you determine who made the router. Try searching the IEEE database of MAC registration blocks for the XX:YY:ZZ part - but replace the colons with dashes; for some reason, the search engine won't do that for you.
Given that information, you can either try searching the machine room to see if there's an XyZZY Networks box with the IP address 192.9.200.66 labeled on the front (or search whatever the manufacturer and IP address are), or can ask the network staff where that router is.
or geolocate
There is no database tracking the geographic location of MAC addresses.