https://file.aiquickdraw.com/mathbot/file/1725678104183avkoxvup.jpg

The image contains a math problem asking to graph the image of a quadrilateral under certain transformations. The specific instructions mention reflecting the quadrilateral over the line \( y = x \).

To help you solve this problem, I'll outline the process for reflecting a shape over the line \( y = x \):

### Steps to Reflect Over \( y = x \):
1. **Identify the coordinates** of each vertex of the quadrilateral. 
2. **Reflect each point** by swapping the x-coordinate with the y-coordinate. If a point is \( (x, y) \), its reflection over \( y = x \) will be \( (y, x) \).
3. **Plot the reflected points** and connect them in the same order as the original quadrilateral to complete the transformation.

Would you like a detailed step-by-step explanation of this process using specific coordinates from the quadrilateral shown in the image? If so, please provide the coordinates or let me know if you'd like help extracting them.

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Here are 5 related questions to expand on this concept:
1. How do you reflect a point over the line \( y = -x \)?
2. What is the general formula for reflecting a point over the x-axis or y-axis?
3. Can you describe a sequence of transformations that includes both a reflection and a rotation?
4. How would reflecting a point over the origin differ from reflecting it over \( y = x \)?
5. What is the effect of a translation followed by a reflection?

**Tip**: When reflecting a shape over a diagonal line like \( y = x \), always remember to swap the x and y coordinates of each vertex to ensure accuracy.

Graph the image of a quadrilateral under the following sequence of transformations. Mention your coordinates clearly around the grid. Reflect over the line y = x.

Learn how to graph a quadrilateral after reflecting it over the line y = x. This problem involves key concepts in coordinate geometry, focusing on transformations and reflections, and is suitable for students in Grades 7-10.

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