📚 Topic Summary
Dilations involve enlarging or reducing a figure by a scale factor with respect to a center point. When the center of dilation is not at the origin (0,0), we need to adjust our approach slightly. Essentially, we translate the figure so the center of dilation is at the origin, perform the dilation, and then translate the figure back. This ensures accurate transformations.
This worksheet will provide practice in applying these transformations, reinforcing understanding of coordinate geometry and transformations. The aim is to solidify your ability to perform dilations accurately, regardless of the center's location.
🧮 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Scale Factor |
A. A transformation that enlarges or reduces a figure. |
| 2. Center of Dilation |
B. The point about which a figure is enlarged or reduced. |
| 3. Dilation |
C. The ratio of the new figure's size to the original figure's size. |
| 4. Image |
D. The resulting figure after a transformation. |
| 5. Pre-image |
E. The original figure before a transformation. |
Match the correct term to the definition: 1-C, 2-B, 3-A, 4-D, 5-E
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
When performing a dilation with a center not at the origin, we first __________ the figure so that the center of dilation is at the __________. Then, we apply the __________ using the given __________ factor. Finally, we __________ the figure back to its original position.
Answer: Translate, origin, dilation, scale, translate
🤔 Part C: Critical Thinking
Explain in your own words why it is necessary to translate a figure when performing a dilation with a center not at the origin. What happens if you don't translate?
Answer: Translating ensures the dilation is performed relative to the correct center. Without translating, the dilation would be centered at the origin, leading to an incorrect transformation of the figure.