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GeoGebra Lab 14

Using GeoGebra, you will consider the transformation called a dilation.

  1. Open a new GeoGebra sketch and graph the points \(C = (1, 4)\), \(P = (5, 2)\) and \(P' = (13, −2)\).
  2. Find the lengths of segments \(CP\) and \(CP'\) by using the Distance tool, then calculate the ratio of \(CP'/CP\) by using a calculator or by entering "s = CP' / CP" into GeoGebra. What is the ratio? This is called the scale factor of the dilation.
  3. Draw \(\Delta ABD\) with \(A = (2,5)\), \(B = (4,4)\), and \(D = (4,3)\). Use the Dilate From Point tool in the Transformations toolbox to dilate \(\Delta ABD\) with \(C\) as the center and with a variable, \(f\), as the scale factor. To do this, select the tool and then click on the triangle, then the point \(C\), and type “f” for the factor. Click “Create Sliders” when prompted.
  4. Move the slider so that the scale factor \(f\) is the same as the scale factor that you found in step B.
  5. Calculate the ratio \(CA' / CA\) the same way that you did in step B.
  6. Calculate the ratio of similarity between the triangle and its image. Enter the values of the ratio of similarity and the ratio \(CA' / CA\) in a text box.
  7. What can be said about the relationship between vectors \(\overrightarrow {CP} \) and \(\overrightarrow{CP'}\), \(\overrightarrow{CA}\) and \(\overrightarrow{CA'}\), and \(\overrightarrow {AB} \) and \(\overrightarrow{A'B'}\)?
  8. If \(R' = (−2, −2)\), what were the coordinates of \(R\), its pre-image, using the same center of dilation? Hint: dilations can also make images closer to the center of dilation.
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