The rule given is $(x, y) \to (13x, 13y)$, which describes a dilation transformation with a scale factor of 13. This means that every point of triangle ABC is scaled by a factor of 13 to form triangle A′B′C′.

Since the scale factor is greater than 1 (specifically, 13), triangle A′B′C′ will be larger than triangle ABC.

Thus, the correct statement is:

A. Triangle A′B′C′ is larger than triangle ABC, because the scale factor is greater than 1.

Would you like more details on dilations or scale factors? Here are some related questions:

1. What is the effect of a scale factor less than 1 on a shape?
2. How can you determine the size of a dilated shape if given the scale factor?
3. What happens to the perimeter of a triangle when the scale factor is 13?
4. How do you apply dilations on each vertex of a polygon?
5. What are the properties of similar triangles resulting from a dilation?

Tip: To calculate the new coordinates of any point after a dilation, simply multiply each original coordinate by the scale factor.