The problem involves determining the scale factor of the dilation between two rectangles $FGHI$ and $F'G'H'I'$.

Step-by-step Solution:

1. Locate the Coordinates of Rectangle $FGHI$ (the original rectangle):

   • $F = (2, -2)$
   • $G = (4, -2)$
   • $H = (4, 4)$
   • $I = (2, 4)$

2. Locate the Coordinates of Rectangle $F'G'H'I'$ (the dilated rectangle):

   • $F' = (6, -6)$
   • $G' = (12, -6)$
   • $H' = (12, 12)$
   • $I' = (6, 12)$

3. Check the Dilation Formula: The scale factor of dilation is calculated by comparing the distances between corresponding points on the two rectangles.

   • Distance between $F$ and $G$ in the original rectangle: $FG = 4 - 2 = 2$
   • Distance between $F'$ and $G'$ in the dilated rectangle: $F'G' = 12 - 6 = 6$

4. Calculate the Scale Factor: The scale factor $k$ is given by: $k = \frac{\text{Distance in dilated figure}}{\text{Distance in original figure}} = \frac{6}{2} = 3$

So, the scale factor of the dilation is 3.

Would you like more details on this process or have any further questions?

Related Questions:

1. How do you calculate the scale factor for a dilation?
2. What is the general formula for dilation on a coordinate plane?
3. How does the scale factor affect the area of the figure?
4. What happens when the scale factor is less than 1?
5. How can you check if a dilation preserves orientation?

Tip:

Always check the distances between corresponding points when dealing with dilations to confirm the scale factor.