https://file.aiquickdraw.com/mathbot/file/1726798735768xp9mk5di.jpg

The task requires reflecting the triangle \( \triangle FGH \) over the line \( y = x \).

1. **Coordinates of the Original Points**:
   - \( F = (-5, 2) \)
   - \( G = (3, 4) \)
   - \( H = (-2, 8) \)

2. **Reflection over the line \( y = x \)**:
   - When reflecting a point \( (x, y) \) over the line \( y = x \), the coordinates of the reflected point become \( (y, x) \).
   
3. **New Coordinates after Reflection**:
   - \( F' = (2, -5) \)
   - \( G' = (4, 3) \)
   - \( H' = (8, -2) \)

You can now plot the new points \( F'(2, -5) \), \( G'(4, 3) \), and \( H'(8, -2) \) on the graph to complete the reflection of \( \triangle FGH \) over the line \( y = x \).

Would you like a more detailed explanation of any part of this process?

### Relative Questions:
1. How do you reflect a point over the \( y \)-axis?
2. What happens when you reflect a shape over the line \( y = -x \)?
3. Can you explain how to reflect a point over any arbitrary line?
4. How do you determine the distance between a point and the line of reflection?
5. What is the result of reflecting a shape over the origin?

### Tip:
When reflecting points over \( y = x \), always swap the \( x \)- and \( y \)-coordinates of each point.

Graph the image of triangle FGH after a reflection over the line y = x.

Learn how to reflect triangle FGH over the line y = x. This problem involves transforming geometric shapes using the concept of reflection and provides a detailed explanation of how to compute the new coordinates of the reflected points.

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