Explanation of Orientation in Transformations
Date: 05/24/2007 at 08:20:15 From: Laura Subject: What is orientation? We've been learning about transformations; translations, reflections, rotations, and dilations, and my teacher keeps saying that a translation, a rotation, and a dilation preserve the orientation. I'm confused as to what orientation is. I think it has to do with naming the triangle. My teacher has mentioned about naming them clockwise or counter-clockwise. I've looked for it in our book, but it's not explained. Could you help?
Date: 05/24/2007 at 22:43:29 From: Doctor Peterson Subject: Re: What is orientation? Hi, Laura. Imagine making a triangle out of paper that is, say, white on one side and black on the other. Avoid making it isosceles. Here's mine: A \ \ \ \ \ \ C---------------B Now if you slide it around (translate it) or turn it (rotate it), or look at it through a magnifying glass (dilate it), it will still have the white side up, and if you go from A to B to C you will still be going clockwise. But now reflect it, say in a vertical line. You can only do that with your model by flipping it over (so the black side is now up): A | A \ \ | /XXX/ \ \ | /XXXXXXX/ \ \ | /XXXXXXXXXXX/ C---------------B | B---------------C We can see in two ways that its orientation is different: we had to turn it over; and when we go from A to B to C now, we are going counterclockwise. And that difference is what we call "orientation". If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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