https://file.aiquickdraw.com/mathbot/file/1727477395471vadn6ik8.jpg

To reflect the figure \(EFGH\) across the **y-axis**, we follow these steps:

1. **Identify the coordinates of the vertices**:
   - \( E \) is at \( (4, 5) \),
   - \( F \) is at \( (5, 5) \),
   - \( G \) is at \( (3, 2) \),
   - \( H \) is at \( (2, 4) \).

2. **Apply the reflection across the y-axis**:  
   When reflecting a point \((x, y)\) across the y-axis, the new coordinates become \((-x, y)\).

3. **Reflect the points**:
   - Reflect \( E(4, 5) \) → \( E'(-4, 5) \),
   - Reflect \( F(5, 5) \) → \( F'(-5, 5) \),
   - Reflect \( G(3, 2) \) → \( G'(-3, 2) \),
   - Reflect \( H(2, 4) \) → \( H'(-2, 4) \).

4. **Plot the new points** to visualize the reflected figure. The reflected shape will look the same as the original but on the left side of the y-axis.

Would you like further details or a breakdown on reflecting shapes? 

Here are 5 related questions to deepen your understanding:
1. What are the rules for reflecting across the x-axis?
2. How would the figure change if reflected across the origin?
3. How do reflections differ from translations or rotations?
4. Can you calculate the distance between any corresponding points before and after reflection?
5. How would you reflect this figure across the line \(x = 1\)?

**Tip**: Reflections preserve the shape and size of figures but reverse their orientation.

Learn how to reflect the figure EFGH across the y-axis with step-by-step instructions. This problem involves geometry concepts such as reflections on the coordinate plane, and is suitable for students in Grades 7-9.

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