Photo Corners

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Sandylion OUR CAT FRAMES BORDERS CORNERS ACCENT Photo Scrapbooking Stickers P06 $0.99 Time Remaining: 5d 14h 28m

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3L Scrapbook Adhesives Photo Corners Black 250 per box $2.69 Time Remaining: 28d 9h 42m Buy It Now for only: $2.69

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How to determine the coordination of a point in a photo with known coordinations for its corners?

I have a photo which I have its size in pixels and X and Y coordination of all of its four corners.

It depends upon the needed accuracy that you wish to give the pixel locations.
Your corner points are almost aligned E-W at the top edge, missing only by a few arcseconds of latitude. If one degree of latitude is approximately (25000/360) or 69 statute miles, then the error of 6.23 arcseconds is an error of (69)6.23/3600 miles.
This photo is centered at about 40.5 degrees from the equator. So the longitude lines are converging, and are not 69 miles apart. At 40.5 degrees latitiude, each degree of longitude is less than 69 miles, or (pi/180)cosA(R), where A is the angle of latitude, and R is the radius of the Earth. That computes for 40.5 degrees to (3.1416/180)(0.7604)(3998mi) or 53.06 miles per degree of longitude.
The left edge is aligned N-S almost as close, 10.24 arcseconds error.
Where things don't align very well is at the right side and bottom edge, where it is 33m21.15s or 2001.15 arcsec or (53.06)2001.15/3600 miles too far east and 16m22.09s or 982.09 arcsec or (69)982.09/3600 miles too far south.
This alignment shows the distances from pixel to pixel grow as they approach the lower right corner. This distortion may be due to the non-perpendicularity of the imaging plane to the surface. But for most of the photo, you can be fairly sure that calculations would be of an accuracy that errors are not large.
How to calculate? The width of the top edge is 1d7m3.03s of arc, or 4023.03 arcseconds, or (53.06)4023.03/3600 miles. With a pixel count of 1400, then each pixel would be (53.06/1400)(4023.03/3600)miles wide. Thus, the calculation for a pixel should be (53.06/1400)(4023.03/3600)miles wide.
The height of the left edge is 1d31m36.4s or 5496.4 arcseconds or (69)5496.4/3600 miles tall. With a pixel count of 900, then each pixel would be (69/900)(5496.4/3600) miles high, and is independent of latitude.