Transformations of Figures through Space!

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Presentation transcript:

Transformations of Figures through Space! The world is not flat.

We Live in a 3 Dimensional World! When you write or draw on paper, you are constructing 2 dimensional figures. Figures that only have height and width. If could actually turn them to the side, they would disappear. Check out the racer! See what I mean!

We all Know that there is Depth in the World. Along with height and width there is thickness or depth. We live in a 3-D World. Which means that in addition to moving figures up and down, you can also move them out and in. If it looks like it’s coming right out at you, it’s probably because it really is! But of course, this is stuff you already know.

3D on a 2D Power Point Now I’m not complaining, but you’re going to have to stay with me on this, because it can be awfully hard to demonstrate three dimensions on a two dimensional Power Point. So you are going to have to use your mind’s eye, your imagination, and want to see the 3 dimensional figures.

Transformations through Space! Remember your transformations? Well let’s see! Which transformation changes the size of a figure? A dilation. Which transformation turns a figure? A rotation. Which transformation slides figure? A translation.

What do you think we’ll get if we translate a triangle through space?. How about a triangular prism?.

What do you think we’ll get if we translate a rectangle through space? How about a rectangular prism?

What do you think we’ll get if we translate a circle through space? How about a cylinder?

What do you think we’ll get if we dilate a square through space? Could this actually be a pyramid?

Lets’ flip it so we can see it from its side? Can you see it now? It’s a pyramid.

What do you think we’ll get if we dilate a circle through space? Could this actually be a cone?

Lets’ flip it so we can see it from its side? Can you see it now? It’s a cone.

What do you think we’ll get if we rotate a triangle through space? Could this possibly be a cone?

Let’s Spin and See! With rotation, that triangle becomes a cone.

What do you think we’ll get if we rotate a rectangle through space? Could this possibly be a cylinder?

Let’s Spin and See! With rotation, that rectangle becomes a cylinder.

What do you think we’ll get if we rotate a circle through space? Could this possibly be a sphere?

Let’s Spin and See! With rotation, that circle becomes a sphere.

So what did we pick up from all of this? When we translate into space what do we get? Prisms and Cylinders When we dilate into space what do we get? Pyramids and Cones. When we rotate into space what do we get? Cones, Cylinders, and Spheres.