To identify the sequence of transformations applied to the preimage $A$ to get the image $A'$, let's analyze the transformations step-by-step:

1. Reflection Check: The preimage $A$ is in the first quadrant. The image $A'$ appears in the second quadrant, suggesting a reflection over the $y$-axis. Reflecting $A$ across the $y$-axis would use the rule $(x, y) \rightarrow (-x, y)$. This matches option B.

2. Rotation Check: After reflecting, $A'$ would be in the second quadrant. To get $A'$ in the correct position (in the second quadrant but rotated), we can apply a rotation:

   • A 90° counterclockwise rotation around the origin (option C) would place $A'$ in the correct orientation in the second quadrant.

Thus, the correct answers are:

• 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 a deeper explanation of any of these transformations or their effects?

Here are some follow-up questions to expand your understanding:

1. How do you determine when to use reflection versus rotation for transformations?
2. What are the rules for other types of reflections (e.g., over the $x$-axis or line $y = x$)?
3. How does a translation differ from rotation and reflection in terms of coordinate transformations?
4. Why does rotating an object about the origin change its quadrant and orientation?
5. What are the effects of a 180° rotation compared to a 90° rotation?

Tip: Always verify each transformation step by checking if the coordinates and orientation match the target image.