I've found a 3rd way to get the 4th vertex:
Let denote the known vertices of the square.
The midpoint of the square is M. Then the M has the coordinates:
M is simultaneously the midpoint of BD:
In my opinion this way seems to be the most simple one.
If you make a sketch, the answer is obvious.
If we know the three vertexes of square, can we find the fourth vertex?
Suppose the three given vertices are: .
Code:| D | ♠ | (1,5) : 1 | A ♥ - - - - - . | 3 | | | | C | ♥ (5,3) | :1 | B ♥ - - - - - . | (2,2) 3 | - - + - - - - - - - - - - - - |
Going from to , we move right 3 and up 1.
. . going from to , we again move right 3 and up 1.
Therefore, is located at