If you keep a copy of the AffineTransform you use when you paint the image, you can use AffineTransform. InverseTransform(Point2D ptSrc, Point2D ptDst) to transform a device space coordinate back to user space.
It's not clear exactly how you're rotating and scaling. But you're probably using an AffineTransform. Fortunately, there's a createInverse() method and a inverseTransform() method.
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