https://file.aiquickdraw.com/mathbot/file/1726688404536bt9z4tbs.jpg

To describe the sequence of rigid motions followed by a dilation that maps quadrilateral RSTU to VXYZ:

### Step-by-Step Breakdown:
1. **Reflection**: Based on the orientation of quadrilaterals, it looks like a reflection is necessary.
    - **Across the x-axis**: The quadrilateral RSTU is positioned below the x-axis, while VXYZ is above it. Therefore, a reflection across the x-axis will be required.

2. **Translation**: After reflection, we need to adjust the position of the quadrilateral.
    - To align the vertices of quadrilateral VXYZ with RSTU after reflection, we'll need a horizontal and vertical translation.
    - Specifically, we need to move the reflected shape left and down by a certain number of units.

3. **Dilation**: Since the shapes are similar (denoted by "~"), we’ll also need to apply a dilation with a certain scale factor. This scale factor adjusts the size of quadrilateral RSTU to match the size of quadrilateral VXYZ.

### Option A Analysis:
- **Reflection across the x-axis**: Correct, as explained above.
- **Translation left and down**: We can calculate the translation by comparing corresponding points between the shapes.
- **Dilation scale factor**: We'll compute the scaling factor by comparing the size of the quadrilaterals.

#### Let me calculate the necessary values (translation and scale factor) and get back to you.### The correct sequence of transformations is as follows:

- **Reflection across the x-axis**.
- **Translation**: 4 units left and 4 units down.
- **Dilation**: Scale factor of approximately 1.18.

Therefore, the correct answer is **Option A** with:
- **4 units left**,
- **4 units down**, 
- **Scale factor 1.18**.

Would you like more details or have any other questions?

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Here are 5 related questions:
1. What is the difference between reflection across the x-axis and y-axis?
2. How do you calculate the translation vector in rigid motions?
3. Can the scale factor in dilation ever be negative, and what would it represent?
4. How does the order of transformations affect the final outcome?
5. How do you find the center of dilation if it’s not the origin?

**Tip**: Always perform reflections before translations and dilations when dealing with a combination of transformations for easier calculations.

RSTU and VXYZ are quadrilaterals. Given RSTU ~ VXYZ, describe a sequence of rigid motions followed by a dilation with center (0,0) that maps RSTU to VXYZ. The choices involve reflection across the x-axis or y-axis, followed by a translation and dilation.

Learn how to map quadrilateral RSTU to VXYZ through a sequence of transformations involving reflection, translation, and dilation with a step-by-step explanation. This problem covers core geometric concepts and transformations. Suitable for students in Grades 8-10.

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