Final answer:
The correct labels for the organelles, based on their structure and functions within eukaryotic cells, are J: mitochondrion, K: nucleus, L: cell membrane, and M: vacuole.
Step-by-step explanation:
The student's question regarding which labels correctly identify the organelles can be answered by understanding the structure and function of each organelle within eukaryotic and prokaryotic cells. First, both types of cells have structures such as the cell membrane, which is the outer layer controlling the entry and exit of substances. However, only eukaryotic cells contain a nucleus and mitochondria, which are not found in prokaryotic cells. Mitochondria are referred to as the power plants of the cell because they produce ATP (energy) through cellular respiration. The nucleus is the control center of the cell containing the DNA and is responsible for gene expression. The Golgi apparatus, ribosomes, and rough endoplasmic reticulum work together to synthesize and transport proteins within the cell. Finally, vacuoles serve roles in storage, transport, and sometimes in breakdown of macromolecules in plant cells.
Considering the functions of these organelles and given the options provided, the correct identification is:
a) J: mitochondrion; K: nucleus; L: cell membrane; M: vacuole