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.