Which of the three branches of government is responsible for drawing the lines defining what the government is allowed to do with respect to civil liberties?

I believe the answer is the Legislative branch.
The legislative branch in the Government is responsible for the creation of laws/regulations that exist in the country.
These laws/regulations will determine the right and responsibilities that held by all citizens in that country, hence drew the line  defining what the government is allowed to do 

The used coins.. .

Afine-grained igneous rock forms as a result of slow cooling.