https://file.aiquickdraw.com/mathbot/file/1725544870171ln2w6y8y.jpg

The image shows a geometric figure plotted on a coordinate plane, and the task is to dilate the figure by a factor of 4, centered at the origin.

To solve this:

1. **Dilation formula**: 
   \[
   (x', y') = (k \cdot x, k \cdot y)
   \]
   where \( k \) is the dilation factor (in this case, \( k = 4 \)), and \( (x, y) \) are the original coordinates of each point.

2. **Procedure**:
   - Identify the coordinates of the vertices of the original shape.
   - Multiply the \( x \) and \( y \)-coordinates of each vertex by 4 (the dilation factor).
   - Plot the new points and connect them to form the dilated figure.

Let me know if you would like me to extract the coordinates of the original figure or if you need any further assistance!

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Would you like a detailed explanation for each step or have any specific questions? Here are five related questions that may expand on this topic:

1. What are the coordinates of the original figure's vertices?
2. How would the figure change with a different center of dilation?
3. How do you determine the effect of a negative dilation factor?
4. How would you dilate a figure using a scale factor less than 1?
5. What are some real-life applications of geometric dilations?

**Tip**: When dilating shapes centered at the origin, the process involves simply scaling the coordinates, making calculations straightforward.

The figure below is dilated by a factor of 4 centered at the origin. Plot the resulting image.

Learn how to dilate a geometric figure by a factor of 4, centered at the origin. This problem covers key geometric concepts such as dilation and coordinate transformations. Suitable for students in Grades 8-10.

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