The correct answer is a eukaryote. While it would be an impulse to answer prokaryote since the first thing that will come to our minds if we deal with a microorganism that thrives in extreme environments (i.e. hot thermal vents) will be archea, which are prokaryotes. But in this case, it is clearly specified that the single-celled organism has a nucleus which is the characteristic feature of eukaryotes.
Bacteria is incorrect as bacteria are prokaryotes. Plant is incorrect as all plants are multicellular organisms.
