https://file.aiquickdraw.com/mathbot/file/1725974068481do0osvf4.jpg

To determine if it is possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B, we need to analyze the shapes and their dimensions.

### Step-by-Step Analysis

1. **Count the Units:**
   - Both Polygon A and Polygon B are drawn on a grid. We should start by counting the lengths of their sides in terms of grid units.

2. **Dimensions of Polygon A:**
   - The horizontal segments have lengths: 2, 3, 2.
   - The vertical segments have lengths: 1, 1, 2.

3. **Dimensions of Polygon B:**
   - The horizontal segments have lengths: 4, 6, 4.
   - The vertical segments have lengths: 2, 2, 4.

4. **Check for Scaling Factor:**
   - For Polygon A to be a scaled version of Polygon B, there must exist a consistent scaling factor \( k \) such that every side length of Polygon A, when multiplied by \( k \), matches the corresponding side length of Polygon B.
   
5. **Finding the Scaling Factor:**
   - The horizontal sides:
     - \(2 \times k = 4 \Rightarrow k = 2\)
     - \(3 \times k = 6 \Rightarrow k = 2\)
     - \(2 \times k = 4 \Rightarrow k = 2\)
   - The vertical sides:
     - \(1 \times k = 2 \Rightarrow k = 2\)
     - \(1 \times k = 2 \Rightarrow k = 2\)
     - \(2 \times k = 4 \Rightarrow k = 2\)
   
   All sides confirm that \( k = 2 \).

### Conclusion

Yes, it is possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B. The scaling factor from Polygon A to Polygon B is 2. Therefore, Polygon B is a scaled version of Polygon A by a factor of 2.

Would you like to see a detailed visual representation of the scaling, or do you have any specific questions?

### Related Questions:

1. What is a scale factor in geometry, and how is it applied?
2. How can we determine if two polygons are similar or congruent?
3. What are the properties of similar polygons?
4. Can you always find a scaling factor between two polygons?
5. How does changing the scale of a polygon affect its area and perimeter?

**Tip:** When working with scaling, remember that the lengths of all sides should change by the same factor, but the angles should remain the same to preserve similarity.

Is it possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B?

Explore whether Polygon A and Polygon B can be scaled copies of each other. Learn how to find the scaling factor between two polygons using grid dimensions. Ideal for students in Grades 6-8.

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