Find coordinates with (x,y) points

On this other recent thread, ai_curious explained how the coordinate system works for images. The principles are the same as the normal way you do analytic geometry in a 2D plane but with a different orientation (flipped vertically about the x axis):

The upper left corner of the image has coordinates (0, 0) and increasing x values move to the right on the x axis and increasing y values move down on the y axis.