Reflection - of a polygon
A transformation where each point in a shape appears at an equal distance on the opposite side of a given line - the line of reflection.
Drag any orange dot to move the line of reflection or reshape the triangle.
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.
Things to try
In the diagram above - click 'reset'
Reshape the triangle by dragging the orange dot at any vertex. Note how the image changes.
Press 'reset' then move the line of reflection by dragging the orange dot on the line. Note how the image changes.
Repeat all the above with 'show lines' checked.
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Other transformation topics
(C) 2011 Copyright Math Open Reference. All rights reserved