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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.

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

Learn how to determine the scale factor of dilation for triangle ABC on a coordinate plane. This solution explains how to use the formula for scale factor and compares corresponding sides of the pre-image and image. Suitable for students in Grades 8-10.

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