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We are given two congruent quadrilaterals \(ABCD\) and \(EFGH\), and the task is to determine the correct sequence of transformations for mapping \(ABCD\) to \(EFGH\).

### Observing the figure:
- Quadrilateral \(ABCD\) is located in the first quadrant, while quadrilateral \(EFGH\) is located in the fourth quadrant.
- The shapes are congruent, meaning the transformations should preserve size and shape, but they are located in different quadrants and possibly rotated.

### Answer choices:
1. **Translate figure \(ABCD\) 5 units down. Then rotate the image 90° clockwise about the origin.**
2. **Rotate figure \(ABCD\) 90° clockwise about the origin. Then reflect the image across the y-axis.**
3. **Reflect figure \(ABCD\) across the x-axis. Then rotate the image 90° counterclockwise about the origin.**
4. **Rotate figure \(ABCD\) 90° counterclockwise about the origin. Then translate the image 4 units to the left.**

### Solution:
By analyzing the transformations:
1. **Rotation 90° clockwise** will move quadrilateral \(ABCD\) to a position similar to \(EFGH\) but in the third quadrant, not the fourth.
2. **Reflecting across the y-axis** will then move the shape to the correct location in the fourth quadrant, where \(EFGH\) is located.

Thus, **Option 2** is the correct transformation sequence: *Rotate figure \(ABCD\) 90° clockwise about the origin. Then reflect the image across the y-axis to form congruent figure \(EFGH\).*

Would you like further details or explanations on any part of the solution?

### Related questions:
1. What are the basic properties of congruent figures in geometry?
2. How do rotations affect the coordinates of points on a plane?
3. What is the difference between reflection across the x-axis and the y-axis?
4. How can we use matrices to represent transformations like rotations and reflections?
5. How would the sequence of transformations change if \(ABCD\) was in a different quadrant?

#### Tip: 
When performing a sequence of transformations, always check whether the order of transformations affects the result, as some transformations are not commutative.

Which sequence of transformations can be performed on figure ABCD to show that the figures are congruent?

Understand how to determine the sequence of transformations (rotation and reflection) required to prove that quadrilaterals ABCD and EFGH are congruent. This geometric problem covers essential concepts like congruence, reflection across the y-axis, and rotation about the origin.

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