I'd know that this reflection is accurate without using a coordinate plane by measuring the points to the line on the image and on the pre-image. Each point has to be equidistant to the line of reflection, for example, I'd measure from point "A" to line segment LM, and it would be the same distance from point "A'", which is "A" prime to line segment LM. Also, the line of reflection would create a 90° with any segment connecting any point on the pre-image to the image. You would either have to take a protracter and measure the angle, or even line something up with a 90° angle and see if it overlaps the 90° angle that is supposed to be there.