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The image shows a problem that involves graphing and labeling a figure's image after applying a geometric transformation. The specific transformation for the first question is a **reflection across the line \( y = x \)**. The instructions indicate the need to find the image of a quadrilateral after this reflection.

### Reflection Across \( y = x \)
1. **Rule for Reflection**: When reflecting a point \((x, y)\) across the line \( y = x \), the new coordinates will be \((y, x)\).
   
2. **Vertices Before Reflection**: Based on the image, the vertices of the quadrilateral are labeled as follows:
   - \( K (-3, 5) \)
   - \( L \) (coordinates not fully visible)
   - \( S \) (coordinates not visible)
   - \( X \) (coordinates not visible)

3. **Vertices After Reflection**: Applying the reflection rule:
   - \( K' (5, -3) \) (already shown in the image)
   - \( L' \), \( S' \), and \( X' \) need to be calculated by swapping their x- and y-coordinates.

4. **Next Steps**: To complete the reflection:
   - Find the original coordinates of points \( L \), \( S \), and \( X \).
   - Apply the reflection rule to get \( L' \), \( S' \), and \( X' \).
   - Plot the new points on the graph and connect them to form the reflected image.

Would you like me to work through the complete reflection for all points? 

### Related Questions
1. What are the coordinates of point \( L \) before reflection?
2. How do we find the coordinates for points \( S \) and \( X \) before reflection?
3. What does a reflection over \( y = x \) do to the orientation of a figure?
4. Can a reflection change the size of a figure?
5. How would a reflection over the line \( y = -x \) differ from \( y = x \)?

**Tip**: Reflections over the line \( y = x \) swap the x- and y-coordinates, while reflections over the line \( y = -x \) swap and negate the coordinates: \((x, y) \rightarrow (-y, -x)\).

Graph and label the image of the figure using the transformation: reflection across y = x.

Learn how to graph and label the reflection of a quadrilateral across the line y = x. This problem explores key geometric concepts, including reflections and transformations in coordinate geometry, with a step-by-step solution suitable for Grades 7-9.

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