Altering an Image created by mouse input with Graphics

Okay, I don't know how this will sound because I have a poor handle on Java in general. But is there anyway to alter an image created by mouse inputs, so that it can be moved around? Either, making the image uneditable and contained to a transformable JFrame, or a simple image that is stored as plot points which can then be altered as their own variables? Is anything like this possible in Java? It doesn't matter how simple or rudimentary the solution is, it's for a final project that I'm already being too ambitious for.