https://file.aiquickdraw.com/mathbot/file/1728300937647qmfu9q2f.jpg

Let's solve this reflection problem step by step.

You are asked to reflect the quadrilateral \( ABCD \) across the line \( y = x \). The rule for reflecting a point \( (x, y) \) over the line \( y = x \) is to switch the coordinates, meaning the new point will be \( (y, x) \).

### Part A: Coordinates of \( A'B'C'D' \)
We need to identify the original coordinates of the points \( A \), \( B \), \( C \), and \( D \) from the graph, and then apply the reflection rule.

- Point \( A \): The coordinates of \( A \) appear to be \( (-10, 0) \).
  - Reflecting over \( y = x \), the new coordinates will be \( A' = (0, -10) \).

- Point \( B \): The coordinates of \( B \) are \( (-5, 5) \).
  - Reflecting over \( y = x \), the new coordinates will be \( B' = (5, -5) \).

- Point \( C \): The coordinates of \( C \) are \( (5, 5) \).
  - Reflecting over \( y = x \), the new coordinates will be \( C' = (5, 5) \) (which stays the same).

- Point \( D \): The coordinates of \( D \) are \( (0, -5) \).
  - Reflecting over \( y = x \), the new coordinates will be \( D' = (-5, 0) \).

### Part B: Drawing the Reflection
To complete the task, you would plot the reflected points \( A' \), \( B' \), \( C' \), and \( D' \) on the graph.

### Summary of Reflected Coordinates
- \( A' = (0, -10) \)
- \( B' = (5, -5) \)
- \( C' = (5, 5) \)
- \( D' = (-5, 0) \)

Would you like further details on any part of this reflection process? Let me know if you have questions!

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Here are 5 related questions to expand your understanding:
1. How do you reflect a point across the line \( y = -x \)?
2. What is the general rule for reflecting points across the x-axis and y-axis?
3. How do the properties of a quadrilateral change under reflection?
4. Can reflection change the size of a shape? Why or why not?
5. How would the coordinates change if the reflection was across the y-axis instead?

**Tip:** Remember, reflecting a point over the line \( y = x \) always switches its coordinates!

Use the boxes to enter the coordinates for the resulting Quadrilateral A'B'C'D' after a reflection across the line y = x. Draw the resulting image on the graph.

Learn how to reflect a quadrilateral across the line y = x and find the coordinates of the reflected points. This solution covers transformation principles, reflection formulas, and plotting on a coordinate grid, making it ideal for students in grades 8-10.

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