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.