The timeline object would work well for this, if you don't draw the path.
Like on timeline A system create object redplane, redplane clear all nodes, redplane add node at firstx,firsty, add node at secondx,secondy, add node at thirdx,thirdy, redplane set position on path to 0, redplane start path movement.
On timeline B system create object redplane, redplane clear all nodes, redplane add node at firstx,firsty, add node at secondx,secondy, add node at thirdx,thirdy, redplane set position on path to 0, redplane start path movement.
Then make sure the path is set to curves, etc.