To solve this problem, we need to determine the scale factor of the dilation between rectangle $U'V'W'X'$ and rectangle $UVWX$.

Step-by-Step Solution:

1. Identify Coordinates of Rectangle $UVWX$:

   • From the graph, we can identify the coordinates of the vertices of the larger rectangle $UVWX$:
     • $U(0, -4)$
     • $V(8, -4)$
     • $W(8, -8)$
     • $X(0, -8)$

   This shows that the length of $UVWX$ (from $U$ to $V$) is 8 units, and the width (from $U$ to $X$) is 4 units.

2. Identify Coordinates of Rectangle $U'V'W'X'$:

   • Similarly, for the smaller rectangle $U'V'W'X'$, we can identify the coordinates as:
     • $U'(2, -2)$
     • $V'(6, -2)$
     • $W'(6, -4)$
     • $X'(2, -4)$

   Here, the length of $U'V'W'X'$ (from $U'$ to $V'$) is 4 units, and the width (from $U'$ to $X'$) is 2 units.

3. Determine the Scale Factor:

   • The scale factor $k$ of the dilation is the ratio of the dimensions of the smaller rectangle $U'V'W'X'$ to the larger rectangle $UVWX$.
   • The length scale factor is $\frac{U'V'}{UV} = \frac{4}{8} = \frac{1}{2}$.
   • The width scale factor is $\frac{U'X'}{UX} = \frac{2}{4} = \frac{1}{2}$.

Since both the length and width are scaled by the same factor, the overall scale factor of the dilation is $\frac{1}{2}$.

Final Answer:

The scale factor of the dilation is $\frac{1}{2}$.

Would you like further clarification on any part of this solution, or would you like additional details?

Relative Questions:

1. What happens to the area of a shape when it is dilated by a scale factor?
2. How do you determine the center of dilation from two similar shapes?
3. What is the difference between enlargement and reduction in dilation?
4. How do we find the scale factor if the coordinates of only two points are given?
5. How does a scale factor greater than 1 affect the size of a shape?

Tip:

When calculating a scale factor, ensure you consistently measure corresponding sides to maintain the accuracy of the transformation.