Final answer:
Mitochondria contain unique DNA inherited from the mother, aiding in tracing genealogy due to its rapid mutation rate and maternal inheritance pattern.
Step-by-step explanation:
The cell organelle that carries its own DNA and is passed down from the mother useful for tracing genealogy is the mitochondria. Mitochondrial DNA is unique because it mutates at a rapid rate, making it a valuable tool for studying evolutionary relationships. Furthermore, mitochondrial genomics is particularly fascinating as the mitochondrial DNA in most multicellular organisms is solely inherited from the mother, which is why it is often utilized in genealogical research.