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The correct term for the slender, hair-like extensions used by some parasites for locomotion is flagella. Flagella are long, whip-like structures that can propel organisms through their environment, allowing them to navigate fluids effectively. This mechanism is crucial for many protozoan parasites that need to move within their hosts or surrounding environments to find nutrients or evade the immune response.

In comparison, cilia are shorter and often more numerous than flagella, and while they can also facilitate movement, they generally create a wave-like motion that is different from the propulsion provided by flagella. Pseudopodia are temporary projections of eukaryotic cells, typically involved in movement and feeding, but they are not hair-like in structure. Filaments are not specifically associated with locomotion in the same context as flagella and do not describe a motility structure in this sense. Overall, flagella's design and function make it the appropriate choice for describing locomotion in certain parasitic organisms.