Final answer:
The compromise reached for determining representation by population in the House of Representatives was the Three-Fifths Compromise.
Step-by-step explanation:
The states reached a compromise for the purpose of determining representation by population in the House of Representatives through the Three-Fifths Compromise. This compromise addressed the contentious issue of whether enslaved people should be counted in determining a state's representation in Congress. Under the Three-Fifths Compromise, every five enslaved individuals would be counted as three persons for both taxation and representation purposes. This gave Southern slaveholding states more power in the House of Representatives than if only the free population had been counted, although less power than if all enslaved people had been counted fully.