https://file.aiquickdraw.com/mathbot/file/1724290019222gkdnkj7f.jpg

Determine the type of dilation shown and the scale factor used.

To determine the type of dilation shown in the image and the scale factor used, we'll compare the dimensions of the smaller rectangle \( D \) and the larger rectangle \( D' \).

From the image:
- The dimensions of rectangle \( D \) are \( 8 \times 6 \).
- The dimensions of rectangle \( D' \) are \( 28 \times 21 \).

To find the scale factor, we divide the dimensions of \( D' \) by the corresponding dimensions of \( D \):

\[
\text{Scale factor} = \frac{\text{dimension of } D'}{\text{dimension of } D}
\]

Let's calculate the scale factor for both dimensions:

1. For the length:
\[
\text{Scale factor (length)} = \frac{28}{8} = 3.5
\]

2. For the width:
\[
\text{Scale factor (width)} = \frac{21}{6} = 3.5
\]

Since both the length and width yield the same scale factor, the dilation is uniform, meaning it scales the figure equally in all directions.

### Conclusion:
- **Type of Dilation:** Enlargement (since the scale factor is greater than 1).
- **Scale Factor:** 3.5

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the area of \( D' \) compare to the area of \( D \) given the scale factor?
2. If the scale factor was 0.5, what would be the dimensions of the new rectangle?
3. What is the effect of a scale factor of 1 on the dimensions of a shape?
4. How would you find the perimeter of \( D' \) based on the original rectangle \( D \)?
5. What would happen if a negative scale factor was applied to rectangle \( D \)?

**Tip:** When calculating the area after dilation, the area changes by the square of the scale factor.

Learn how to determine the type of dilation and scale factor in a geometry problem involving rectangles. This problem covers the calculation of scale factors for enlargement and the impact on dimensions. Suitable for students in Grades 7-9.

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