Transformations Overview

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Presentation Description

Translation, Rotation, Dilation, Reflection, and Symmetry are summarized in this PowerPoint show.

Comments

By: sveta1962 (45 month(s) ago)

It is a great presentation. Thank you very much for sharing your work.

By: sandio55 (68 month(s) ago)

Thanks. We actually broke that up in to 5 separate lessons with examples, if that would work better for you than the overview. Let me know and I can post them.

By: amydavis17 (68 month(s) ago)

I really like your overview of transformations. I'll be teaching it to my 7th graders on Tuesday after Christmas break. I'd like to use your powerpoint as my introduction to the lesson. Really good job. (Southaven, MS)

By: lukring (69 month(s) ago)

its for my math class. i really hope for ur positive response about this. ill be waiting. thanks a lot.

By: lukring (69 month(s) ago)

hi, im looking for a powerpoint presentation for my next topic about transformation.i find your file here and i like it. but it shows here that ur not allowing any one to download this file. can i have an access on it? Im a teacher and i need it .

Presentation Transcript

Slide 1: 

Geometry: Math 8

Slide 2: 

To transform something is to change it. In geometry, there are specific ways to describe how a figure is changed. The transformations you will learn about include: Translation Rotation Reflection Dilation

Slide 3: 

A translation "slides" an object a fixed distance in a given direction.  The original object and its translation have the same shape and size, and they face in the same direction. Translations are SLIDES.

Slide 4: 

Let's examine some translations related to coordinate geometry.   The example shows how each vertex moves the same distance in the same direction.

Slide 5: 

In this example, the "slide"  moves the figure7 units to the left and 3 units down.

Slide 6: 

A rotation is a transformation that turns a figure about a fixed point called the center of rotation.  An object and its rotation are the same shape and size, but the figures may be turned in different directions.

Slide 7: 

The concept of rotations can be seen in wallpaper designs, fabrics, and art work.

Slide 8: 

This rotation is 90 degrees counterclockwise.

Slide 9: 

A reflection can be seen in water, in a mirror, in glass, or in a shiny surface.  An object and its reflection have the same shape and size, but the figures face in opposite directions.  In a mirror, for example, right and left are switched.

Slide 11: 

The line (where a mirror may be placed) is called the line of reflection.  The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection. A reflection can be thought of as a "flipping" of an object over the line of reflection.

Slide 12: 

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation used to create an image larger than the original is called an enlargement.  A dilation used to create an image smaller than the original is called a reduction.

Slide 13: 

Dilations always involve a change in size. Notice how EVERY coordinate of the original triangle has been multiplied by the scale factor (x2).

Slide 14: 

REVIEW: Answer each question……………………….. Does this picture show a translation, rotation, dilation, or reflection? Rotation

Slide 15: 

Does this picture show a translation, rotation, dilation, or reflection? Dilation

Slide 16: 

Does this picture show a translation, rotation, dilation, or reflection? (Line) Reflection

Slide 17: 

Which of the following lettered figures are translations of theshape of the purple arrow?  Name ALL that apply. Letters a, c, and e are translations of the purple arrow.

Slide 18: 

Has each picture been rotated in a clockwise or counter-clockwise direction? The birds were rotated clockwise and the fish counterclockwise.

Slide 19: 

Basically, a tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping and no gaps.

Slide 20: 

Dutch graphic artist M. C. Escher (1898-1972) is known for his creative use of tessellations in his work. What transformations can you see in this picture? The birds and fish have been translated here.

Slide 21: 

What transformations can you see in this Escher print? Some birds have been translated and some have been rotated.

Slide 22: 

Can you name examples in real life of each transformation? Translation Rotation Reflection Dilation

Slide 23: 

Check out these sites: http://www.farraguttn.com/fhs/math/nctm/index.htm http://www.mathsnet.net/transformations/index.html http://www.mcescher.com/