A reflection through an axis followed by a reflection across a second axis parallel to the first one results in a total motion which is a translation.

Image via Wikipedia

The discussion at our last MaST meeting about parallel axes of reflections lead me to think about this a lot. And it wasn’t until I sat down with some paper and drew things that I could see it clearly.

At the last meeting, we looked into exploring reflection using a skipping rope and children mirroring each others movements. We looked at reflecting points, with people moving freely and easily with this concept.

We moved on to creating a triangle with three people holding hands. The reflection of this object was made simple by each of the adults matching themselves to someone on the imaging side, each movement was then copied by the imagers so that each point remained the same distance from the axis of reflection.

The major sticking point was when parallel axes of reflection were introduced. We couldn’t agree on how things should be. I actually think, on reflection (pun fully intended) that we got it right straight away and all the discussion only served to confuse things even more.

In the diagram below, the purple line is Reflection Axis 1, the black line is Reflection Axis 2. The lines are parallel, that is lines that do not intersect or meet.

Also, the object is always on the far left, image 1 is middle and image 2 is on the right.

The red lines show the distance between the object and image 1. The blue lines show the distance between image 1 and image 2.

The second diagram shows what has happened after the object has been moved further to the right, away from the first axis of reflection.

As the changes in the coloured lines show, as the object is moved further from reflection axis 1, object 1 moves further away – the length of the red line has increased. As the 1st image moves closer to the 2nd axis of reflection, the 2nd image moves closer to the 2nd reflection line – the length of the blue line has decreased.

Furthermore, the movement of the 2nd image related to the object is the same effect as translation.

So, parallel lines of reflection are fairly straightforward.

One Response to “Parallel axes of reflection”

Leave a Reply

You must be logged in to post a comment.

Calendar
November 2010
M T W T F S S
« Sep   Dec »
1234567
891011121314
15161718192021
22232425262728
2930  
Blog Catalog
Twitter Goodies