The image shows two quadrilaterals, $OPQR$ and $O'P'Q'R'$, along with a question asking to identify the sequence of transformations that maps $OPQR$ onto $O'P'Q'R'$. The transformations to choose from involve translations, rotations, and reflections.

To analyze the transformation:

1. Position of $OPQR$ and $O'P'Q'R'$:

   • $OPQR$ is in the second quadrant (coordinates are negative for $x$-values).
   • $O'P'Q'R'$ is in the first quadrant (positive $x$-values).

2. Possible transformations:

   • Translation: There is a clear shift horizontally and vertically from $OPQR$ to $O'P'Q'R'$.
   • Reflection: Since the shapes are mirrored across either axis (most likely across the $y$-axis).
   • Rotation: It's also possible that a rotation was involved based on their relative positioning.

Examining each choice:

• Option 1: "A translation left 12 units followed by a reflection across the $x$-axis."
  This doesn't seem correct because the shapes are not mirrored across the $x$-axis.

• Option 2: "A rotation 90° clockwise around the origin followed by a translation up 12 units."
  This option seems plausible because rotating $OPQR$ by 90° clockwise would align its orientation with $O'P'Q'R'$, and then a translation upward could place it correctly.

• Option 3: "A translation left 2 units and up 9 units followed by a reflection across the $y$-axis."
  This doesn't seem accurate, as the translation described here doesn't align the two shapes perfectly.

Correct Answer:

Option 2: A rotation of 90° clockwise around the origin, followed by a translation up 12 units, maps $OPQR$ onto $O'P'Q'R'$.

Would you like further details on this transformation process, or do you have any specific questions?

Here are 5 related questions to explore this topic further:

1. How do you determine the center of rotation for a geometric transformation?
2. What are the rules for reflections across the $x$- and $y$-axes?
3. How do you identify if a shape has undergone a translation only?
4. What is the difference between a 90° clockwise and counterclockwise rotation?
5. How can you calculate the distance between corresponding points after a translation?

Tip: When dealing with transformations, always check if a reflection or rotation is involved by comparing the orientation and relative position of corresponding points.