Testing non-collinear points

I plotted points (-2,-2) (2,2) and (5,1) then plugged in x values from -7 to 18 to find the y values of points of symmetry at those x values. I then graphed the (x,y) coordinates of the points.
 

The red markers show where the original three points are, and each is a possible POS.

I'm assuming that when the points can be connected by a curved line, the possible POS form a shape opening in the same direction as the curve. for example, the points in the graph above could be connected by a downward facing shape, and the trend of the POS is also a downward opening curve.