What u. s. policy involved giving money to latin american nations in exchange for support, trade agreements, and nominal control over their affairs?
roosevelt corollary
monroe doctrine
dollar diplomacy
free trade agreement

C) Dollar diplomacy.

Mainly executed during William Taft administration, as you staded in consisted in a "trade" between the US and those Latin American nations. In exchange of investments and money, they requested political support over the US affaires.

In order to help the student expand his/her knowledge I will help answer the question. This in hope that the student will get a piece of knowledge that will help him/her through his/her homework or future tests.

This is a fact. The Dollar Diplomacy involved giving money to Latin American nations in exchange for support, trade agreements, and nominal control over their affairs. Many will confuse this with the Alliance for progress program.  

I hope it helps, Regards.