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 $(x, y) \rightarrow (-y, x)$.

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?

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.