It looks like you uploaded an image containing some geometry problems related to transformations and dilations on a coordinate plane. Let's focus on question 3, as it seems to be the main one from your query:

Question 3: "Given the pre-image and image of triangle ABC, what is the scale factor of dilation?"

Looking at the two triangles in the diagram, the pre-image is the smaller triangle ABC, and the larger triangle is the image after dilation.

To find the scale factor, you can use the formula:

$\text{Scale Factor} = \frac{\text{Length of a side in the image}}{\text{Length of the corresponding side in the pre-image}}$

From the graph:

• Pre-image triangle ABC has a vertical height from point $C(1,1)$ to $A(1,3)$, so the height is 2 units.
• Image triangle (dilated triangle) has a vertical height from point $C'(1,1)$ to $A'(1,9)$, so the height is 8 units.

Thus, the scale factor is:

$\text{Scale Factor} = \frac{8}{2} = 4$

So, the scale factor of the dilation is 4.

Would you like further details or have any additional questions?

Here are 5 related questions:

1. What is the effect of a scale factor greater than 1 on a geometric figure?
2. How can you determine the center of dilation given a pre-image and an image?
3. What would happen to the triangle if the scale factor were less than 1?
4. Can a dilation change the orientation of a figure, and why or why not?
5. What is the formula for dilation in a coordinate plane when the center is not the origin?

Tip: When dealing with dilations, always compare corresponding points or sides to accurately find the scale factor.