Tanton Segment Puzzle

Two line segments, each with a point moving back and forth on it at some uniform speed. Can their midpoint trace a space-filling path? In the interactive figure, you can change the speeds of the points A and B by sliding the appropriate slider at the bottom of the figure. You can click on and drag the points X to change the length, location, and orientation of the segments. You can erase the midpoint trace by clicking on the appropriate button in the lower right corner. You can also click on the Start/Stop animation button to start the motion. Try changing the color of the midpoint and associated trace by sliding the vertical color sliders on the right side.