Final answer:
Acidophiles, which are part of the domains Bacteria and Archaea, are classified as prokaryotes because they lack a true nucleus and membrane-bound organelles.
Step-by-step explanation:
To match the following organism, Acidophiles, to their category amongst Eukaryote, virus, and prokaryote, one must first understand the basic cell structures. Acidophiles belong to domains Bacteria and Archaea, which are classified as prokaryotes. Prokaryotic cells are predominantly single-celled organisms that lack a true nucleus and membrane-bound organelles. Since acidophiles are known to include organisms from these domains, they can be correctly categorized as prokaryotes.