How do Platyhelminthes locomote?

Answer 1

Many flatworms are parasitic, living within the host, and once anchored, have no need for locomotion.

The land and water dwelling species lay down a film of mucus through which their cilia move to aid locomotion. When disturbed, they perform muscular motions, rather like waves, in their attempt to escape. This may be both vertical and horizontal.

A New Zealand species grows up to 15 cm or more, (but more commonly less than 10cm) and is a now serious invader in Europe, killing the native earthworms. This they do by wrapping around their prey and using body fluids to dissolve what they need. At rest they may curl up like a roll, but elongate when needed. These I've seen more commonly at night than in daylight.