https://file.aiquickdraw.com/mathbot/file/17253793729158vtucdsv.jpg

To solve this problem, let's go through the dilation process.

### Problem Breakdown:
- **Original Figure:** ABCD
- **Scale Factor:** 2
- **Center of Dilation:** (0, 0)

### Steps to Dilate the Figure:
1. **Identify the coordinates of the original vertices** of quadrilateral ABCD.
   - Let's denote the vertices as \( A(x_1, y_1) \), \( B(x_2, y_2) \), \( C(x_3, y_3) \), and \( D(x_4, y_4) \).
   - From the image:
     - \( A(-3, 1) \)
     - \( B(-1, 3) \)
     - \( C(1, 3) \)
     - \( D(3, 1) \)

2. **Apply the scale factor** of 2 to each vertex, using the formula:
   \[
   (x', y') = (k \cdot x, k \cdot y)
   \]
   where \( k \) is the scale factor (which is 2 in this case).

   So, the new coordinates will be:
   - \( A'(-6, 2) \)
   - \( B'(-2, 6) \)
   - \( C'(2, 6) \)
   - \( D'(6, 2) \)

3. **Plot the new coordinates** \( A', B', C', D' \) on the graph to form the dilated quadrilateral.

Would you like to proceed with additional details on this process or have any specific questions about it?

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### Relative Questions:
1. What is the general formula for dilating a point with respect to a different center of dilation?
2. How would the shape change if the scale factor was less than 1?
3. What happens to the area of the quadrilateral after dilation with a scale factor of 2?
4. How would the coordinates change if the dilation were centered at a different point, say (1,1)?
5. Can you identify any properties of the quadrilateral that remain unchanged after dilation?

### Tip:
Always double-check the new coordinates after applying the scale factor to ensure accuracy in geometric transformations.

Dilate ABCD with a scale factor of 2 and center (0, 0). Use the Polygon Tool to plot the image.

Learn how to dilate a quadrilateral ABCD by a scale factor of 2 centered at (0, 0). This problem covers essential geometric concepts, including dilation and transformations. Suitable for students in Grades 7-9.

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