Final answer:
Euglena is the correct answer as it is a single-celled organism with a flagellum for movement and a distinct eyespot for light detection.
Step-by-step explanation:
The single-celled organism that moves by a flagellum and has a unique eye spot to detect light is Euglena. Euglena is a protist that possesses a red eyespot used to detect light, which is crucial for their photosynthetic capability. It moves through aquatic habitats with the help of two flagella, one being notably longer than the other.
This organism exhibits a mixotrophic mode of nutrition, meaning it can assimilate food both through photosynthesis and heterotrophically, depending on light availability. In addition to its flagella, Euglena is capable of moving by changing its shape, thanks to a flexible structure known as the pellicle, which is made up of protein bands attached to the cytoskeleton, offering the cell its signature flexibility and form.