To determine the scale factor of the dilation of line segment AB centered at the origin, we can use the coordinates of points A and B before and after the dilation.
-
Identify the original coordinates of points A and B:
- A = (1, -3)
- B = (2, -4)
-
Identify the dilated coordinates of points A and B:
- A' = (4, -12)
- B' = (8, -16)
-
The scale factor \( k \) can be calculated by comparing the coordinates of the original points with their dilated coordinates. The formula for the scale factor is given by: \[ k = \frac{\text{dilated coordinate}}{\text{original coordinate}} \]
Let's calculate the scale factor for point A first:
-
For point A: \[ k_A = \frac{4}{1} = 4 \]
-
For point B: \[ k_B = \frac{8}{2} = 4 \]
Since the scale factors \( k_A \) and \( k_B \) are both equal to \( 4 \), we conclude that the scale factor used in the dilation of line segment AB, centered at the origin, is:
\[ \boxed{4} \]