Easily done in Java, especially if you don't need to do anything other than put a dot or X where the mouse clicks.
Load the image and you can write directly to the image if you load it as a BufferedImage. Look at that API and you can see that you can get the Graphics object of a BufferedImage. Java uses the Graphics object to do any graphic functions so look at the API for Graphics.
You can load the image using ImageIO from the javax library. You can do a draw Image onto a JPanel Graphics object by overriding paintComponet of a JPanel. Other than those things you'll just need to use MouseListener to get the click event to show the coordinates to where the mouse position was when it was clicked.
load the image into a BufferedImage using ImageIO.
make a custom JPanel (extend JPanel) and override the paintComponent.
use the Graphics object of the JPanel to do paint the image onto the JPanel background (drawImage)
use the MouseListener to get the click event to get where the mouse pointer position was when it was clicked.
draw the "X" or whatever onto the BufferedImage
call repaint on your JPanel so your updated image will be drawn on the background
go get an A on your assignment
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