https://file.aiquickdraw.com/mathbot/file/1726922918272hgj1fdlf.jpg

The image you provided shows a problem where you are asked to plot the image of a figure \( ABCDEFGH \) after a dilation with a scale factor of \( \frac{1}{3} \). One side of the figure, segment \( AH \), has already been plotted.

To proceed with this dilation:

### Steps to Perform the Dilation:
1. **Identify the Coordinates**: Determine the coordinates of all points \( A, B, C, D, E, F, G, H \) in the original figure.
2. **Apply the Scale Factor**: Since the scale factor is \( \frac{1}{3} \), multiply the coordinates of each point by \( \frac{1}{3} \) to get the new coordinates after dilation.
   - For example, if point \( A \) has coordinates \( (x_A, y_A) \), its new coordinates will be \( \left(\frac{x_A}{3}, \frac{y_A}{3}\right) \).
3. **Plot the New Points**: Using the new coordinates for points \( A', B', C', \dots H' \), plot the dilated figure.

### Important Points:
- **Center of Dilation**: It's important to check where the center of dilation is located. Typically, if it's not specified, the origin (0, 0) is assumed to be the center.
- **Line Segment Scaling**: The length of each side will be reduced to one-third of its original length after dilation.

Let me know if you'd like further clarification on dilation or any other aspect of this problem!

### Follow-up Questions:
1. How do you calculate the coordinates of a point after dilation?
2. What is the significance of the center of dilation?
3. How does dilation affect the angles of a polygon?
4. Can dilation produce a congruent figure? Why or why not?
5. What are some real-life examples where dilation occurs?

**Tip**: Always double-check the scale factor to ensure the transformation is applied correctly.

Plot the image of Figure ABCDEFGH after a dilation with scale factor 1/3. One of the sides has been plotted for you.

Learn how to plot the image of Figure ABCDEFGH after a dilation with a scale factor of 1/3. This problem involves identifying the coordinates, applying the dilation formula, and plotting the new points on the grid. Suitable for students in Grades 8-10.

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