https://file.aiquickdraw.com/mathbot/file/1729025615639jvdz2mak.jpg

The problem involves identifying a sequence of transformations that move the original square \( A \) (located in the first quadrant) to two new images: \( A' \) and \( A'' \).

Let's walk through the transformations based on the visual positions:

1. **From \( A \) to \( A' \)**:
   - \( A \) is reflected over the **y-axis**, since the image \( A' \) appears symmetrically in the second quadrant.
     - Reflection rule: \( (x, y) \rightarrow (-x, y) \).
   
2. **From \( A' \) to \( A'' \)**:
   - After the reflection, \( A' \) is rotated **90° counterclockwise** about the origin.
     - This rotation places \( A' \) into the third quadrant, resulting in \( A'' \).
     - Rotation rule: A 90° counterclockwise rotation transforms \( (x, y) \rightarrow (-y, x) \).

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### Correct Answers:
- **B**: First, \( A \) was reflected using the rule \( (x, y) \rightarrow (-x, y) \).
- **C**: Second, \( A' \) was rotated 90° counterclockwise about the origin.

Would you like further clarification or help with other parts?

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### 5 Related Questions:
1. What is the rule for rotating a point 180° about the origin?
2. How do reflections differ across the x-axis vs. y-axis?
3. What is the effect of rotating a shape 270° counterclockwise?
4. Can translations occur after rotations without affecting the result?
5. How do you determine if a transformation preserves the orientation of a shape?

**Tip:** Always use transformation rules step-by-step to ensure accuracy when working with multiple transformations.

Identify the sequence of transformations that were applied to the preimage to get the image.

Learn how to identify transformations, such as reflections over the y-axis and 90-degree counterclockwise rotations, with a step-by-step breakdown of the transformations applied to a square in the coordinate plane.

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