https://file.aiquickdraw.com/mathbot/file/1728929123974pur75zlb.jpg

To find the scale factor, we need to compare the sizes of the original triangle (black) to the transformed triangle (red).

### Step-by-Step Solution:

1. **Identify corresponding points**:
   - The black triangle has points \( R, S, T \).
   - The red triangle has points \( R', S', T' \), which are the images of \( R, S, T \) after the transformation.

2. **Find distances**:
   - Measure the distance between two corresponding points. For example, measure the distance between \( R \) and \( S \) on the black triangle, then between \( R' \) and \( S' \) on the red triangle.

3. **Compute the scale factor**:
   The scale factor is the ratio of the corresponding distances:
   \[
   \text{Scale Factor} = \frac{\text{Length of } R'S'}{\text{Length of } RS}
   \]

Upon inspecting the grid, we find:
- Distance between \( R \) and \( S \) (black triangle) = 2 units.
- Distance between \( R' \) and \( S' \) (red triangle) = 4 units.

Thus, the scale factor is:
\[
\frac{4}{2} = 2
\]

The scale factor is **2**.

Would you like more details or have any other questions? 

Here are five related questions:
1. How does a scale factor affect the perimeter of a shape?
2. What is the area ratio when a figure is enlarged by a scale factor of 2?
3. Can a scale factor be negative, and what would that imply geometrically?
4. How do you calculate the scale factor between two non-congruent shapes?
5. What is the relationship between scale factor and similarity in geometric shapes?

**Tip**: When working with dilations, always check if the transformation preserves angle measures, as this ensures the figures are similar.

What is the scale factor between the black and red triangles?

This problem involves finding the scale factor between two triangles using dilation. The red triangle is the image of the black triangle. By measuring corresponding side lengths and applying the scale factor formula, the problem is solved with a scale factor of 2. Suitable for students in Grades 8-10.

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