The principle of Representative Government is important to maintain balance of power, by making it so people are important to the government. Representative Government helps make the government more fair for the people because they're involved in what happens. For example, article 3, section 2, clause 1, of the Constitution, is judicial power helps laws be what the people want. Also, in article 1, section 2, clause 1, of the Constitution follows this, because the people vote for who is going to be in the House of Representatives.
The principle of Separation of Powers is important because it helps the government not get controlled by only one branch. Separation of Power allows the branches to have different powers. Which is needed to have a government where the power is equally balanced. For example, in article 1, section 8, all clauses, of the Constitution lists all of the powers congress has. While another example is article 2, section 2, clause 1, the president is the commander of the army and navy.