Dilation is a transformation that changes the size of a figure. It requires a center point and a scale factor. The center of dilation is the fixed point from which the figure is enlarged or reduced. The scale factor determines how much larger or smaller the image becomes. If the scale factor is greater than 1, the image is an enlargement. If the scale factor is between 0 and 1, the image is a reduction.
Understanding the center of dilation is crucial because it serves as the reference point for all changes in size. Imagine placing a light bulb at the center; the shadow it casts will be larger or smaller depending on how far away the object is. That point where the light bulb sits? That's your center of dilation!
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Center of Dilation | A. The ratio of the lengths of the corresponding sides of the image and pre-image. |
| 2. Scale Factor | B. A transformation that changes the size of a figure. |
| 3. Dilation | C. The fixed point from which dilation occurs. |
| 4. Image | D. The new figure after a transformation. |
| 5. Pre-image | E. The original figure before a transformation. |
Complete the following sentences using the words: enlargement, reduction, scale factor, center of dilation, dilation.
Explain in your own words how changing the center of dilation affects the position of the dilated image. Provide an example.
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