Under the terms of the great compromise, how would the members of the house of representatives be chosen? by the state legislatures, based on population by the state legislatures, with each state having equal representation by a vote of the people, based on population by a vote of the people, with each state having equal representation

Correct  by a vote of the people, based on population.

Explanation/detail:

The Great Compromise was a measure decided during the United States Constitutional Convention in 1787.  The Great Compromise resolved a dispute between small population states and large population states.  The large population states wanted representation in Congress to be based on a state's population size. (This was the essence of the Virginia Plan.) The smaller states feared this would lead to unchecked dominance by the big states; they wanted all states to receive the same amount of representation.  (This was the New Jersey Plan.)

The Great Compromise (aka Connecticut Compromise) created a bicameral (two-chamber) legislature, with different rules for representation in each chamber. Representation in the House of Representatives would be based on population.  In the Senate, all states would have the same amount of representation, by two Senators.

by a vote of the people, based on population

Explanation:

I have no clue just took a test and it says its right

hope it helps

btw @MrZieleniewo has it right first lol

have a nice day! <3