To find the scale factor of the dilation, we need to compare the coordinates of corresponding points in the original and the dilated rectangle. The scale factor (k) tells us how much the size of the original figure is enlarged or reduced to form the new figure.

The formula for the scale factor is:

$k = \frac{\text{New coordinate value}}{\text{Original coordinate value}}$

Let's use the coordinates of one pair of corresponding points. We can pick the point $E$ and its corresponding point $E'$:

• Original point: $E (-3, 3)$
• Dilated point: $E' (-9, 9)$

For the x-coordinate:

$k_x = \frac{-9}{-3} = 3$

For the y-coordinate:

$k_y = \frac{9}{3} = 3$

Since both the x and y coordinates have the same scale factor, the scale factor for the dilation is 3.

Thus, the scale factor of the dilation is 3.

Would you like further clarification on how this works, or do you have other questions? Here are some related questions:

1. How do you identify corresponding points in dilations?
2. How does the scale factor affect the area of the figure?
3. What happens to the perimeter of a figure after dilation?
4. How do you find the center of dilation?
5. What would happen if the scale factor was less than 1?

Tip: When dealing with dilations, the center of dilation is key to determining how the figure transforms. The distance between corresponding points increases or decreases in direct proportion to the scale factor.