To determine the scale factor used for the dilation from triangle ABC to triangle A'B'C', we can look at the coordinates of corresponding points before and after dilation.
For point A to A':
- Point A: A(-3, -3)
- Point A': A'(-12, -12)
To find the scale factor, we divide the coordinates of A' by the coordinates of A. Let's take one coordinate (either x or y, they will be the same for this calculation):
\[ \text{Scale Factor} = \frac{A'}{A} = \frac{-12}{-3} = 4 \]
We can verify this by checking other points:
For point B to B':
- Point B: B(3, 3)
- Point B': B'(12, 12)
\[ \text{Scale Factor} = \frac{B'}{B} = \frac{12}{3} = 4 \]
And for point C to C':
- Point C: C(0, 3)
- Point C': C'(0, 12)
\[ \text{Scale Factor} = \frac{C'}{C} = \frac{12}{3} = 4 \quad (\text{0 remains 0, so only y-coordinate matters here}) \]
Thus, the scale factor is consistently calculated to be 4.
The scale factor used for the dilation from triangle ABC to triangle A'B'C' is 4.