The correct response is C: the Constitution was amended, changing the way that the Vice President was elected.
The presidential election of 1800, which resulted in Thomas Jefferson's victory over John Adams, led to significant political changes. One of those changes was the subsequent ratification of the 12th Amendment in 1804, which established a new procedure for electing the President and Vice President, ensuring that both were elected on separate ballots rather than the previous method where the runner-up became Vice President.
Responses A and B do not accurately relate to the immediate consequences of the 1800 election. The U.S. went to war with Britain in 1812, and the Monroe Doctrine was issued in 1823, long after the election of 1800.