To flip any of the points to map up correctly to the other points, you would have to do a reflection over the y-axis. The reasoning for this is because you cannot dilate your shape because it won't map over correctly. A translation will not work, mainly because the shape still needs to flip. A rotation will also not work because when you rotate it, the shape will still not map over your new one.
-So your answer to this question would be that only a Reflection over the y-axis will allow the two shapes to map over each other correctly.