Transformations

Transformations can be used to describe the movement in a plane.  Check out the PowerPoint used to explain the different types of transformations described in our textbook.

Using GSP to Investigate Transformations

• You can translate an object in GSP by any distance and angle or by any marked vector.  Click on the link below and follow the directions in order to translate the image.  When you moved the pre-image (the original F), what effect did it have on the other translated images?  Move point B and watch the image that was translated by the vector.  What happened?  Did the images moving linearly?  Did the images change shape, size or direction?

• You can rotate an object in GSP by a center or by a marked angle.  Click on the link below and follow the directions in order to rotate the image.  When you moved the pre-image (the original F), what effect did it have on the other rotated images?  Move the center and observe the effect.  What happened?  Did the images moving linearly?  Did the images change shape, size or direction?

• You can reflect an object in GSP by marking a mirror.  Click on the link below and follow the directions in order to reflect the image.  Move the pre-image again and observe the effect.  Move line segment AB (the marked mirror) and observe the effect.  What happened?  Did the images moving linearly?  Did the images change shape, size or direction?

• You can dilate an object by marking a center and a fixed ratio.  Click on the link below and follow the directions in order to dilate the image.  Move the pre-image again and observe the effect. Move the center and observe the effect.  What happened?  Did the images moving linearly?  Did the images change shape, size or direction?

TRANSLATION

ROTATION

REFLECTION

DILATION

• Now open GSP create an image and translate, rotate, reflect and dilate the image on your own.  Color code the different images.  Play around with them and see what happens.  What must you do in order to move the images back to the pre-image?

Let's Go to the Movies!

Transformations are used in computer special effects to make movies.  Create a movie flip book of your own on paper.  Draw a square TV screen and make the origin the center of the television.  Put an image on the paper, translate the image to start the action you want it to do. For example, running or jumping.  Put the new image on the second page.  Continue to do that for about 10 pages.  Make each image move a little at a time.  When you are finished bind all the papers together, flip your book quickly and watch your images come to life!  How do filmmakers use transformations and computers to make movies?  What are pixels and how are they used?  As you find links on the topic email me so I can add them to my web page.  A number of video sources explain computer graphics as well.  Computer Dreams by Digital Vision Entertainment is one source.

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