https://file.aiquickdraw.com/mathbot/file/1727188154208a31hktop.jpg

Let's analyze the transformations shown in the images one by one. You are asked to identify the type of transformation: **rotation**, **reflection**, **translation**, or **dilation**.

1. **Image a)**: The pre-image is reflected across the **y-axis**. Since the dashed figure is on the right side and the solid figure appears symmetrically on the left side of the y-axis, this is a **reflection** over the y-axis.
   
2. **Image b)**: The pre-image (dashed) is moved to a different location without rotating or flipping. This is a simple **translation**, as the shape remains unchanged and is simply shifted along the coordinate plane.

3. **Image c)**: The pre-image is rotated around the origin. It seems to have undergone a **rotation of 90° clockwise**.

4. **Image d)**: The dashed figure (pre-image) is scaled down to a smaller size, with the corresponding points aligned proportionally. This is a **dilation** (a reduction), as the figure's size changes but the shape remains the same.

### Summary of transformations:
- a) Reflection
- b) Translation
- c) Rotation
- d) Dilation

Would you like further explanations or details on these types of transformations?

Here are 5 related questions to expand your understanding:
1. How do you mathematically represent a reflection across the x-axis or y-axis?
2. What is the formula for rotating a point by 90 degrees clockwise or counterclockwise?
3. Can a dilation change the orientation of a figure? Why or why not?
4. How would you describe a translation in terms of vector notation?
5. What is the difference between rotation and reflection in terms of transformation properties?

**Tip**: When identifying transformations, check whether the size, orientation, or position changes, as each type of transformation affects these properties differently.

Name the type of transformation (rotation, reflection, translation, or dilation) depicted in the diagram below, where the dashed figure represents the pre-image and the solid figure represents the image.

Learn how to identify geometric transformations such as reflection, rotation, translation, and dilation in coordinate planes. This problem covers key geometry concepts and is suitable for students in Grades 7-9.

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