Reflection
The reflection of figure ABCDE over the line y=x can be proven accurate without the use of a coordinate plane because each vertex and its image are the same distance from the line of reflection. In a reflection, the pre-image and image must be equidistant from the line of reflection. A line connecting any point on the pre-image with the image will form a 90 degree angle with the line of reflection and be perpendicularly bisected by it. Since the pre-image ABCDE and image A’B’C’D’E’ can be mapped back onto each other over the line of reflection, this reflection is accurate.