Hold on, lemme whip out my handy-dandy POCKET CONSTITUTION. Lol, I'm sorry. I just finished AP Government. Anyway.
Amendments I through IX (1 through 9) all discuss the rights of the people that shall not be abridged by Congress. However, the 10th amendment talks about the right of the States. None of the other amendments in the BoR even mention State's rights. In fact, only the 2nd and 6th amendments even contain the word "State"! In summation, the 10th amendment is specifically so that the federal government does not abridge the rights of the States.
Hope this helps!