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.