An african american man drinking at a water container with a sign labeled
© akg-images / universal images group/image quest 2013

the policy of segregation illustrated in this image taken in 1939 was determined to be

constitutional in the case of plessy v. ferguson in 1896
unconstitutional in the case of plessy v. ferguson in 1896
unconstitutional by the case of brown v. board of education
constitutional by the case of brown v. board of education

The policy of segregation illustrated in this image taken in 1939 was determined to be  constitutional in the case of Plessy v. Ferguson in 1896.

Explanation:

The case Plessy v. Ferguson of 1896 is a legal decision in the jurisprudence of the Supreme Court of the United States in which it was decided to maintain the constitutionality of racial segregation even in public places (especially in rail networks) under the doctrine of «Separated but equal».

The verdict of seven votes to one was announced, with the majority opinion drafted by Judge Henry Billings Brown and dissent by John Marshall Harlan. David Josiah Brewer did not participate in the decision. "Separated but equal" remained in US law until its challenge in 1954 by the ruling of the Supreme Court in Brown v. Board of Education

b) a state law could be declared illegal if it contradicted the constitution.

explanation:

the conflict of this case originated when james w. mcculloch, a cashier of the baltimore branch of the second bank of the united states that the congress had chartered in 1816, refused to pay a tax imposed by the maryland state.

in the case, the state of maryland appealed that the establishment of a second bank was unconstitutional since the constitution didn't say anything about granting that power to congress. however, the case determined that even if such right wasn't specifically stated in the constitution, it was part of the "implied powers" of the government enunciated in article i, section 8.

the case also eliminated maryland's legislation to impose taxes to a national bank, asserting that even though the states retained the power of taxation, the constitution's laws are supreme and can not be controlled by the states, therefore, if a state law contradicts the constitution, it should be declared illegal.

explanation: