JTextArea cannot accept anything except for "plain text" (no images/movies, all text is formatted exactly the same).
If you want, you can try using a JEditorPane (or JTextPane) as both of these components support formatted text (either RTF, HTML, or your own formatting) as well as images/movies/etc. However, from looking over your project specifications the easiest way to draw a picture is to use a JLabel and set it to contain an Icon.
See: How to Use Labels (The Java™ Tutorials > Creating a GUI With JFC/Swing > Using Swing Components)
and How to Use Icons (The Java™ Tutorials > Creating a GUI With JFC/Swing > Using Swing Components)
Your actionPerformed method doesn't need to change the JLabel, simply create an ImageIcon for the three pictures and change the icon for the JLabel using the setIcon() method