Final answer:
A unicellular, eukaryotic, photosynthetic organism fits in Domain Eukarya, specifically within Kingdom Protista, due to its nucleus-containing cells and diversity including photosynthetic members.
Step-by-step explanation:
An organism that is unicellular, eukaryotic, and photosynthetic belongs to the Domain Eukarya and is most likely part of the Kingdom Protista. This domain includes all organisms whose cells have a nucleus and other membrane-bound organelles, which differentiates it from the prokaryotic domains of Bacteria and Archaea.
Within the eukaryotes, protists are a diverse kingdom that includes both photosynthetic organisms, like algae, and non-photosynthetic organisms. This is because, while the organism is photosynthetic and thus capable of producing its own food like plants, it is also unicellular, which differentiates it from the multicellular organisms found in Kingdom Plantae.