https://file.aiquickdraw.com/mathbot/file/17303132330042t5848yg.jpg

To solve this reflection problem, we need to reflect each point of the figure over the x-axis.

### Step-by-Step Solution:

1. **Identify the coordinates of points Z, W, X, and Y** from the original image:
   - \( Z \) is at \( (-8, 2) \)
   - \( W \) is at \( (-4, 1) \)
   - \( X \) is at \( (1, 3) \)
   - \( Y \) is at \( (-3, 4) \)

2. **Apply the reflection rule over the x-axis**:
   - Reflecting a point \( (x, y) \) over the x-axis changes the \( y \)-coordinate’s sign, resulting in \( (x, -y) \).

3. **Determine the coordinates of the reflected points**:
   - The reflection of \( Z(-8, 2) \) will be \( Z'(-8, -2) \).
   - The reflection of \( W(-4, 1) \) will be \( W'(-4, -1) \).
   - The reflection of \( X(1, 3) \) will be \( X'(1, -3) \).
   - The reflection of \( Y(-3, 4) \) will be \( Y'(-3, -4) \).

4. **Plot these new points** on the graph:
   - Place \( Z' \), \( W' \), \( X' \), and \( Y' \) at their respective reflected coordinates.
   - Connect the points \( Z' \), \( W' \), \( X' \), and \( Y' \) in the same order as the original shape.

This will create the reflection of the figure over the x-axis.

Would you like a visual representation or have any specific questions about this solution?

### Further Related Questions:
1. How do you find the reflection of a point over the y-axis?
2. What is the rule for reflecting a point over the origin?
3. How would you reflect a shape over a line like \( y = x \)?
4. Can you apply the same method to find a reflection over other lines?
5. How do reflections affect the orientation of shapes?

**Tip:** When reflecting over the x-axis, only the y-coordinates change, flipping to their opposite values.

Graph the image of the figure below on a reflection over the x-axis.

Learn how to reflect a geometric figure over the x-axis. This problem guides you through identifying the coordinates of each point, applying the reflection formula, and graphing the reflected points for accuracy. Ideal for students in Grades 8-10 studying coordinate geometry.

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