Dilation Properties

Author:
Eric Karnowski
Topic:
Dilation
GeoGebra Applet
  1. Click on the “Show Lines” box. Make the following changes and pay attention to the relationship between the two lines. [list=2]
  2. Change the scale factor. Be sure to look at values greater than 1 and values less than 1, as well as a scale factor of 1. You can even try some negative scale factors.
  3. Drag the Center to different locations. Put it to the left of both lines, inside the original triangle, on line AB, and to the right of both lines.
  4. Finally, drag some of the vertices of the original triangle that form one of the lines (A and B) to different locations. Try putting either in the same place as the Center.
What do you notice about the relation between the two lines, line AB and its image line A'B'?
  • Unclick the “Show Lines” box and click the “Show Side Lengths and Areas” box. Position A at (1, 8), B at (1, 4), and C at (-2, 4) to begin, so the side lengths are whole numbers. Then make the following changes and pay attention to the relationships between side lengths in the original triangle and the corresponding side lengths of the image. [list=2]
  • Change the scale factor. Be sure to look at values greater than 1 and values less than 1, as well as a scale factor of 1. You can even try some negative scale factors.
  • Drag the Center to different locations. Put it to the left of both lines, inside the original triangle, on line AB, and to the right of both lines.
  • Finally, drag some of the vertices of the original triangle that form one of the lines (A and B) to different locations. Try putting either in the same place as the Center. [/list] What do you notice about the relation between the side lengths of the original triangle and the corresponding side lengths of the image triangle?[/list] If you finish early, think about how you might justify your observations mathematically. Why must those things be true?

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