This is an example of a reflection. In my example I reflected blue polygon ABCD over the y-axis to get red polygon A'B'C'D'. To reflect an image without using a coordinate plane you can use patty paper and copy the image with the line of reflection. After you had copied the image and line you flip the patty paper to the other side and line up the line with the line on your patty paper, having the image on the opposite side where you want it reflected. Scribble hardly on the outline of your image and lift your patty paper up. You should get a light outline of the reflected image. You can check your work by making sure all the points line up and all points on image 1 and reflected image 2 are equal distance from the line of reflection.