If there was an image on the paper then you would need to reduce both the horizontal and vertical axis by equal amounts otherwise you will distort the image (no rotating the paper 90 degrees won't work)
So trust me the correct answer to the question "What is 1/4 the size of A4?" is A8
I'm fairly certain images dont change the physical dimensions of an object or there inter-relationship with other ISO defined dimensions of similar objects. However, if you quoted the wrong post then that's understandable!