https://file.aiquickdraw.com/mathbot/file/1729221572036jtz68l4a.jpg

To determine the scale factor, we need to compare corresponding sides of the two shapes, since the two figures appear to be scaled versions of one another. 

1. First, let's confirm which side on the smaller figure (right) corresponds to segment \(DG\) on the larger figure (left). From the diagram and the question, the corresponding side appears to be \(RU\) on the smaller figure.

2. Now, we need to calculate the scale factor by comparing the lengths of these corresponding sides:
   - Measure the length of \(DG\) on the left figure.
   - Measure the length of \(RU\) on the right figure.
   - The scale factor will be the ratio of these lengths: 
   
   \[
   \text{Scale Factor} = \frac{\text{Length of } RU}{\text{Length of } DG}
   \]

If you want, I can analyze the lengths in detail or help guide you through the steps of manually measuring them from the grid.

Do you need help with the side lengths, or are you able to measure them from the image directly?

Here are 5 questions that might help you expand on this topic:
1. Can we calculate the scale factor for other corresponding sides of the trapezoid?
2. How do we know which sides are corresponding?
3. What would the areas of the two figures be based on the scale factor?
4. How does the scale factor affect perimeter comparison between the two figures?
5. What are some real-life applications of scale factors?

**Tip:** When comparing figures, always ensure you're working with corresponding sides that are aligned similarly in shape and position.

Learn how to calculate the scale factor between two similar quadrilateral figures. Understand the concept of corresponding sides and use the formula for scale factor. This problem is suitable for students in Grades 7-9.

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