To find the scale factor of the dilation, we need to compare the distances between corresponding points in the original and dilated triangles.

Given:

• Original points: $A(0,0), B(0,4), C(6,0)$
• Dilated points: $A'(0,0), B'(0,10), C'(15,0)$

1. Calculate the distance from $A$ to $B$ in the original triangle: $AB = |4 - 0| = 4$

2. Calculate the distance from $A'$ to $B'$ in the dilated triangle: $A'B' = |10 - 0| = 10$

3. Find the scale factor by dividing the length in the dilated triangle by the length in the original triangle: $\text{Scale factor} = \frac{A'B'}{AB} = \frac{10}{4} = 2.5$

Therefore, the correct answer is B) 2.5.

Would you like further details on any part of this explanation?

Here are five related questions to consider:

1. How would the scale factor change if one of the original points were different?
2. Can a scale factor be less than 1? What does it represent geometrically?
3. How do you calculate scale factors for non-origin-centered dilations?
4. What happens to the area of the triangle after a dilation with a scale factor of 2.5?
5. How can we verify the dilation is consistent across all points?

Tip: When performing dilations, always ensure each side length scales proportionally to verify consistency.