The authority for this is found in Article one of the US Constitution.
Representatives need to be at least 25 years old (compared to 30 for senators), and seven years a citizen (compared to nine years for senators). They must be residents within their states at the time of their election, but do not necessarily have to live within their districts.
In the 2012 election, the Republicans came in and took the House. Since then, they like to blame Obama for everything. Oh and they gerrymandered all the districts so they'd win, even if nobody liked them. They even shutdown the government in one big temper tantrum where a lot of people forgot the meaning of the word "compromise." Just like the Republicans to remind us that the word Congress has more than one meaning.
Opinion polling has found that sixty percent of Americans would fire every single member of congress, including their own representative. A separate poll found that congress is less popular than colonoscopies, lice, used car salesmen, traffic jams, NFL replacement refs, root canals (yes, root canals).. Now that we've been through a government shutdown, there's a chance telemarketers, meth labs, and even playground bullies are more popular than a Republican Congress (not to mention North Korea).