Final answer:
The Supreme Court's decision in Plessy v. Ferguson was largely based on the rights granted in the Fourteenth Amendment, which guarantees equal protection under the law. The court ruled that the segregation law did not violate the equal protection principle because it provided separate but equal facilities for different races.
Step-by-step explanation:
In the case of Plessy v. Ferguson, the Supreme Court's decision was largely based on the rights granted in the Fourteenth Amendment. The Fourteenth Amendment to the U.S. Constitution guarantees equal protection under the law and prohibits states from denying any person within their jurisdiction the equal protection of the laws.
In Plessy v. Ferguson, Homer Plessy argued that the Louisiana segregation law violated the principle of equal protection, but the Supreme Court disagreed. They ruled that the law was not a violation of the equal protection principle because it provided separate but equal facilities for different races. This decision upheld the legality of segregation and allowed states to continue enforcing racial segregation laws.