The three blue points always lie on a straight line. The blue points are the closest points to the moving red point on the lines. In other words the blue points are the projections of the moving red point to the lines.
Mirror Squares
10² = 100 <-> 001 = 01²
11² = 121 <-> 121 = 11²
12² = 144 <-> 441 = 21²
13² = 169 <-> 961 = 31²
