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

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honestly i love the walking dead, mainly the quotes. “well, pardon me young man, excuse the [insert bad word here] out of my gosh darn french, but did you just threaten me? ” sksk (of course it's not the exact words)