In this transformation, we start with a given shape. In the figure above the original shape is the yellow triangle on the left. We also have a line of reflection (the vertical line in the figure) which acts like a mirror. Every point on the original triangle is "reflected" in the mirror and appears on the right side an equal distance from the line.
In the figure above click 'reset'. Note how the point A in the original appears on the right as A' and is an equal distance from the line as A. The same goes for B and any other point on the original triangle. To see this more clearly, click on 'show distances'. You can see that the distance from A to the line is the same as the distance from line to A'. Move the line of reflection and convince yourself this is always so.
The net result of all this is that the original shape is transformed to a mirror image an equal distance on the other side of the line of reflection. We say that the gray triangle A'B'C' is the "reflected image over the line PQ" of the yellow triangle ABC on the left.
The line of reflection is always the perpendicular bisector of the lines linking corresponding points in the original and the image. Click on 'show distances' to see this.