https://file.aiquickdraw.com/mathbot/file/1725594163981g6cuw4pw.jpg

The problem asks to graph the image of parallelogram KLMN after a dilation with a scale factor of 4, centered at the origin.

### Steps to solve:

1. **Identify Coordinates**: First, we need to determine the coordinates of the points \( K \), \( L \), \( M \), and \( N \) from the image before dilation.

   - The coordinates appear to be approximately:
     - \( K(0, 2) \)
     - \( L(-2, 4) \)
     - \( M(2, 6) \)
     - \( N(4, 4) \)

2. **Apply the Scale Factor**: Since the dilation is centered at the origin, each coordinate will be multiplied by the scale factor (4).

   The new coordinates after dilation will be:
   - \( K'(0 \times 4, 2 \times 4) = (0, 8) \)
   - \( L'(-2 \times 4, 4 \times 4) = (-8, 16) \)
   - \( M'(2 \times 4, 6 \times 4) = (8, 24) \)
   - \( N'(4 \times 4, 4 \times 4) = (16, 16) \)

3. **Plot the New Points**: To graph the new parallelogram:
   - Plot the points \( K'(0, 8) \), \( L'(-8, 16) \), \( M'(8, 24) \), and \( N'(16, 16) \).
   - Connect these points to form the dilated parallelogram.

This is the process to dilate the given parallelogram by a factor of 4.

Would you like further explanation on any part of the process or details about graphing?

### Related Questions:
1. What happens when the center of dilation is not at the origin?
2. How does changing the scale factor affect the size and orientation of the parallelogram?
3. What would happen if the dilation had a negative scale factor?
4. How do you find the area of the dilated parallelogram?
5. How can you determine the coordinates of points after dilation without a graph?

**Tip**: Always check the center of dilation; if it's not at the origin, the process of multiplying coordinates changes slightly.

Graph the image of parallelogram KLMN after a dilation with a scale factor of 4, centered at the origin.

Learn how to dilate parallelogram KLMN by a scale factor of 4, centered at the origin. This problem covers key geometry concepts including dilation, scale factor, and plotting new coordinates after transformation. Suitable for students in Grades 8-10.

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