Given that segment $UV$ is dilated by a scale factor of 22 to form segment $U'V'$, and the length of $UV$ is 66, we need to find the length of $U'V'$.

The relationship between the original segment $UV$ and the dilated segment $U'V'$ is given by the formula:

$U'V' = \text{scale factor} \times UV$

Substituting the given values:

$U'V' = 22 \times 66 = 1452$

So, the length of $U'V'$ is 1452 units.

Would you like more details or have any questions?

Here are some related questions:

1. What is dilation in geometry?
2. How does the scale factor affect the size of a figure?
3. Can dilation result in a smaller figure, and how?
4. What are some real-world applications of dilation?
5. How do you find the center of dilation?

Tip: When working with dilations, always remember that a scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.