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.