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The problem in the image asks to reflect a shape across the line \( y = x \), and find the coordinates of the new points after the reflection.

### Reflection across the line \( y = x \):
When reflecting a point \( (x, y) \) across the line \( y = x \), the coordinates of the reflected point become \( (y, x) \). In other words, the x- and y-coordinates swap places.

Let's find the new coordinates of points \( P \), \( Q \), \( H \), and \( L \) after the reflection.

- **Point P** has coordinates \( P(x_1, y_1) \).
- **Point Q** has coordinates \( Q(x_2, y_2) \).
- **Point H** has coordinates \( H(x_3, y_3) \).
- **Point L** has coordinates \( L(x_4, y_4) \).

After the reflection, the new points \( P' \), \( Q' \), \( H' \), and \( L' \) will be:

- \( P' = (y_1, x_1) \)
- \( Q' = (y_2, x_2) \)
- \( H' = (y_3, x_3) \)
- \( L' = (y_4, x_4) \)

Let me extract the exact coordinates of the points from the image and compute their reflections.The image shows the points \( P \), \( Q \), \( H \), and \( L \) on the coordinate plane. I'll now determine the coordinates of these points visually and then calculate their reflections across the line \( y = x \).

### Coordinates from the image:

1. **P** is at \( (-4, -3) \).
2. **Q** is at \( (-2, 0) \).
3. **H** is at \( (-2, 3) \).
4. **L** is at \( (1, 0) \).

### Reflections across \( y = x \):
1. **P'**: Reflect \( (-4, -3) \) to get \( (-3, -4) \).
2. **Q'**: Reflect \( (-2, 0) \) to get \( (0, -2) \).
3. **H'**: Reflect \( (-2, 3) \) to get \( (3, -2) \).
4. **L'**: Reflect \( (1, 0) \) to get \( (0, 1) \).

### Final coordinates after reflection:
- \( P' = (-3, -4) \)
- \( Q' = (0, -2) \)
- \( H' = (3, -2) \)
- \( L' = (0, 1) \)

Would you like a more detailed explanation on the reflection process or the next steps? Here are five related questions to explore further:

1. How would the transformation change if reflected across the \( y \)-axis instead?
2. What are the properties of a reflection across any arbitrary line \( y = mx + c \)?
3. How can we describe a reflection algebraically in terms of matrix transformations?
4. What happens to the area and orientation of a shape after a reflection?
5. How do multiple reflections (e.g., over \( y = x \) and \( x \)-axis) combine?

**Tip**: Always check the orientation of points before and after reflection, especially in cases involving complex figures or transformations.

Find the image after the given transformation: Reflection across y = x.

Learn how to find the image of a shape after reflecting across the line y = x. This problem involves reflecting points P, Q, H, and L on the coordinate plane and finding their new coordinates using the formula (x, y) -> (y, x). Suitable for Grades 8-10.

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