Hello! I posted this question the other day but when my friends and I compared our answers, some of them said their answer is only 4 and not ±4 like what I arrived at. The question and my solution to the problem are attached as pictures.

Shouldn't it be ±4 because whether A is (1,-4) or (1,4), its distance to the midpoint of D and Y will still be 4?

If not, can you please tell me where I went wrong?

Thank you very much for your help!