The key to describing dilations is knowing the scale factor that relates the preimage, or the original object, to the image, or the enlarged or reduced object. In this part of the lesson, you will investigate how to determine the scale factor that is being used for a given dilation.
Click on the screenshot below and use the interactive tool to dilate quadrilateral A. The slider that is labeled "Scale Factor" controls the scale factor used to generate the purple quadrilateral, B, from the red quadrilateral, A. Record your observations in your notes.
Interactive popup. Assistance may be required.Click on the 2D tab found on the upper right hand corner of the interactive.
Click on the red rectangle in the lower left-hand corner. Use the scale factor slider to change the size of the purple shape in relation to the red one.
The dimensions of the red shape can be changed by clicking and dragging a green vertex. Graphs and measures can be observed on the right panel by clicking on the tabs.
What do you notice about the ratio of the lengths of two corresponding sides and the scale factor of the dilation?
Interactive popup. Assistance may be required. The ratio of the lengths of two corresponding sides is equal to the scale factor used to create the dilation.
If you know the lengths of two corresponding sides in two similar figures, how can you determine the scale factor?
Interactive popup. Assistance may be required. Divide the length of the dilated side by the length of the original side.
Use the interactive to complete the following table. For each of the given scale factors, click in the cell to indicate if that scale factor generates an enlargement or a reduction.
How can you determine whether a scale factor will generate an enlargement or a reduction?
Interactive popup. Assistance may be required. If the scale factor is between 0 and 1, the dilation will be a reduction.
For each of the following pairs of similar figures, determine the scale factor that can be used to generate the dilation from the original figure.
