https://file.aiquickdraw.com/mathbot/file/1727229809626ejtonaqf.jpg

To solve this problem, you need to reflect the given figure over the x-axis and then answer the true or false statements based on the reflection. Here's a step-by-step guide on how to do it:

### Step 1: Understand Reflection Over the X-Axis
Reflecting a figure over the x-axis means that each point of the figure will "flip" across the x-axis. Specifically, the y-coordinate of each point will change its sign, while the x-coordinate will remain the same.

For example:
- If a point is at (x, y), its reflection over the x-axis will be (x, -y).

### Step 2: Apply the Reflection to Each Point
You will need to reflect the vertices **W**, **X**, **Y**, and **Z** over the x-axis. Based on the image you provided, here are the coordinates of the points before reflection:
- **W** is at (-7, 1)
- **X** is at (-4, 5)
- **Y** is at (1, 5)
- **Z** is at (1, 1)

After reflecting over the x-axis, their new coordinates will be:
- **W'** will be (-7, -1)
- **X'** will be (-4, -5)
- **Y'** will be (1, -5)
- **Z'** will be (1, -1)

### Step 3: Graph the Reflected Points
Now, you can plot these new points on the graph:
- **W'** at (-7, -1)
- **X'** at (-4, -5)
- **Y'** at (1, -5)
- **Z'** at (1, -1)

Once the points are plotted, connect them to form the reflected shape.

### Step 4: Answer the Questions
1. **The corresponding sides in the pre-image and image are congruent.**
   - Reflecting a figure over the x-axis does not change its size or shape, so the sides of the original and reflected figures will be congruent. This statement is **true**.

2. **The reflection changed the orientation of the vertices.**
   - Reflection does indeed change the orientation of the figure. In this case, the order of the vertices (W, X, Y, Z) will be reversed after reflection. This statement is **true**.

Would you like to go over the plotting of points or any specific detail?

Here are 5 related questions to help deepen understanding:
1. What happens to the coordinates when reflecting a point over the y-axis instead of the x-axis?
2. How do you perform a reflection over the origin?
3. What is the difference between reflecting a shape and rotating it?
4. How can you determine if two shapes are congruent after a transformation?
5. What other transformations can be combined with reflections to achieve different effects?

**Tip:** Always check both the size and orientation of shapes when verifying congruence and transformations.

Reflect the figure over the x-axis. Then, mark the statements as true or false.

Learn how to reflect a figure over the x-axis and answer questions about congruence and orientation. This transformation problem covers key geometric concepts like coordinate reflection and properties of congruent figures, suitable for Grades 6-8.

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