Reflection over a line

Pictured above, is a reflection of shape ABCDEFG across the y-axis. The resulting image is labeled A'B'C'D'E'FG'. The properties that make this transformation a reflection are...the pre-image and the image have the same side lengths and same angle measures...each pair of corresponding points are equidistant to the y-axis. Without a coordinate plane the line of reflection in this transformation would be found by connecting two corresponding points and then finding that connecting line's perpendicular bisector. In this case the line of reflection happens to run through points B and G. When each pair of corresonding points is connected and each perpendicular bisector is found, if all the perpendicular bisectors line up on top of each other than the transformation is a reflection.