If I did not have a coordinate plane, I would know that this rigid motion is accurate by carefully checking the reflection, and then the rotation. I would make sure that all points on the reflected image are equidistant from the line of reflection, which it reflected over. I would also make sure that the line of reflection forms a [math]90^{\circ}[/math]angle with the connecting segments from the pre-image to the image. On the rotation I would make sure that the angle of rotation is the same on each point on the object, which it should be unless the angles, or the length of the lines on the shape changed. Most of all, I would make sure that each point on the image kept the same distance from the center of rotation.