About this video
Sal reviews the rigid transformations (translation, rotation and reflection), where lengths between points are preserved. He then introduces dilation, a non-rigid transformation that scales a figure up or down so lengths change.
You'll be able to
- name the three rigid transformations.
- explain that a dilation scales a figure up or down.
- explain why a dilation is not a rigid transformation.
Key words
- Rigid transformation
- A transformation where the lengths between points stay the same.
- Non-rigid transformation
- A transformation where lengths between points can change.
- Dilation
- A transformation that scales a figure up or down, making it bigger or smaller.
- Translation
- Shifting a figure without turning or flipping it.
Transcript
- [Instructor] In previous videos, we started talking about the idea of transformations. In particular, we talked about rigid transformations. So for example, you can shift something. This would be a translation. So the thing that I'm moving around is a translation of our original triangle.
You could have a rotation. So that thing that I translated, I am now rotating it as you see right over there. And you can also have a reflection. The tool that I'm using doesn't make reflection too easy. But that's essentially flipping it over a line. But what we're going to talk about in this video is a non-rigid transformation.
And what makes something a rigid transformation is that lengths between points are reserved. But in a non-rigid transformation, those lengths do not need to be preserved. So for example, this rotated and translated triangle that I'm moving around right here, in fact I'm continuing to translate it as I talk.
I can dilate it. And one way to think about dilation is that we're just scaling it down or scaling it up. So for example, here, I am scaling it down. That is a dilation. Or I can scale it up. This is also a dilation or even going off of the graph paper. So the whole point here's just to appreciate that we don't just have the rigid transformations, we can have other types of transformations, and a dilation is one of them in your toolkit that you will often see, especially when you get introduced to the idea of transformation.
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