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The diagram shows two congruent quadrilaterals, \( ABCD \) and \( EFGH \), on a coordinate grid, and the question is asking which sequence of transformations can be performed on \( ABCD \) to form \( EFGH \).

Looking at the diagram, we can see that quadrilateral \( ABCD \) is located in the second quadrant, while \( EFGH \) is located in the fourth quadrant. Since the two figures are congruent, their sizes and shapes are the same, meaning we only need to determine the transformation sequence (translation, rotation, reflection, etc.).

Let's analyze the options:

1. **Translate figure \( ABCD \) 5 units down. Then rotate the image 90° clockwise about the origin to form congruent figure \( EFGH \)**: 
   - Translating \( ABCD \) 5 units down moves the quadrilateral, but it would still be in the second quadrant. A 90° clockwise rotation would not align it with \( EFGH \), so this option is incorrect.

2. **Rotate figure \( ABCD \) 90° clockwise about the origin. Then reflect the image across the y-axis to form congruent figure \( EFGH \)**:
   - Rotating 90° clockwise would move \( ABCD \) into the fourth quadrant, and reflecting across the y-axis could potentially align it with \( EFGH \). This is a promising option.

3. **Reflect figure \( ABCD \) across the x-axis. Then rotate the image 90° counterclockwise about the origin to form congruent figure \( EFGH \)**:
   - Reflecting across the x-axis would place the figure in the third quadrant, and a 90° counterclockwise rotation would move it to the first quadrant, so this option is incorrect.

4. **Rotate figure \( ABCD \) 90° counterclockwise about the origin. Then translate the image 4 units to the left to form congruent figure \( EFGH \)**:
   - Rotating 90° counterclockwise would move \( ABCD \) into the first quadrant, and translating 4 units left would not align it with \( EFGH \), so this option is incorrect.

The correct answer is:  
**Rotate figure \( ABCD \) 90° clockwise about the origin. Then reflect the image across the y-axis to form congruent figure \( EFGH \)**.

Would you like more details or have any further questions? Here are some related questions to expand the topic:

1. What is the difference between rotation and reflection in geometric transformations?
2. How can you determine if two shapes are congruent on a coordinate plane?
3. What effect does a 90° rotation have on a figure on a coordinate plane?
4. What transformations would move a figure across multiple quadrants on a coordinate plane?
5. How do you combine different transformations to achieve a desired position?

**Tip:** When combining transformations, consider the order of operations. The sequence matters in determining the final position of the figure.

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

Learn how to transform quadrilateral ABCD into its congruent counterpart EFGH through a series of geometric transformations. This problem covers key concepts in geometric transformations including rotation, reflection, and translation. Suitable for students in Grades 6-8.

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