Transformations of Figures through Space!

1
Transformations of Figures through Space!

• The world is not flat.

2
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!

3
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 its coming right out at you,
  its probably because it really is!
• But of course, this is stuff you already know.

4
3D on a 2D Power Point

• Now Im not complaining, but youre 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 minds eye,
  your imagination, and want to see the 3
  dimensional figures.

5
Transformations through Space!

• Remember your transformations? Well lets see!
• Which transformation changes the size of a
  figure?
• A dilation.
• Which transformation turns a figure?
• A rotation.
• Which transformation slides figure?
• A translation.

6
What do you think well get if we translate a
triangle through space?.

• How about a triangular prism?.

7
What do you think well get if we translate a
rectangle through space?

• How about a rectangular prism?

8
What do you think well get if we translate a
circle through space?

• How about a cylinder?

9
What do you think well get if we dilate a square
through space?

• Could this actually be a pyramid?

10
Lets flip it so we can see it from its side?

• Can you see it now? Its a pyramid.

11
What do you think well get if we dilate a circle
through space?

• Could this actually be a cone?

12
Lets flip it so we can see it from its side?

• Can you see it now? Its a cone.

13
What do you think well get if we rotate a
triangle through space?

• Could this possibly be a cone?

14
Lets Spin and See!

• With rotation, that triangle becomes a cone.

15
What do you think well get if we rotate a
rectangle through space?

• Could this possibly be a cylinder?

16
Lets Spin and See!

• With rotation, that rectangle becomes a cylinder.

17
What do you think well get if we rotate a circle
through space?

• Could this possibly be a sphere?

18
Lets Spin and See!

• With rotation, that circle becomes a sphere.

19
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.