The Parallelogram Factory

Can you make any shape parallelogram by dragging the dark blue dot? Why or why not? Can you prove your answer? Can you generate rectangles by moving the BLUE point? If you think so, describe how you would move the BLUE point to generate a family of rectangles. Can you generate rhombuses by moving the BLUE point? If you think so, describe how you would move the BLUE point to generate a family of rhombuses.