Let the points be A(a,b) and B(c,d). Calculate the slope of AB. Multiply it by -1 to get the slope of a line perpendicular to AB. This slope is tan theta for the perpendicular line . Now , calculate AB distance =r, and use P(x,y)=P(a+r*cos theta,b+r*sin theta). Similarly generate the fourth vertex of the square.

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You can take a diagonal and rotate it 90 degrees. So finally from (x1; y1) and (x2; y2) you get:

x3 = (x1 + x2 + y1 — y2) / 2; y3 = (y1 + y2 + x2 — x1) / 2

x4 = (x1 + x2 + y2 — y1) / 2; y4 = (y1 + y2 + x1 — x2) / 2

and if you have two points of one side then you can get:

x3 = x1 — y2 + y1; y3 = y1 — x1 + x2;

x4 = x2 — y2 + y1; y4 = y2 — x1 + x2;

or

x3 = x1 + y2 — y1; y3 = y1 + x1 — x2;

x4 = x2 + y2 — y1; y4 = y2 + x1 — x2;