Help with a problem involving distance and midpoint?

Sep 2018
27
0
Philippines
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!
 

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Plato

MHF Helper
Aug 2006
22,474
8,643
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?
You are correct. $k=\pm 4$.