To find the coordinates of points A' and B' after dilation of points A and B with a scale factor of 13 centered at the origin, we use the formula for dilation:
\[ (x', y') = (k \cdot x, k \cdot y) \]
where \( k \) is the scale factor and \( (x, y) \) are the original coordinates.
For point A (-6, 3):
- A' = (13 * -6, 13 * 3) = (-78, 39)
For point B (-12, 9):
- B' = (13 * -12, 13 * 9) = (-156, 117)
So the correct coordinates after dilation are:
A'(−78, 39) and B'(−156, 117)
However, none of the response options provided match this calculation. It appears all choices provided do not represent the points after dilation correctly. If we had to pick from provided options, we would need to calculate based on either reviewing the problem constraints or confirming the scale factor should have been different.
Please double-check if the scale factor given is precisely 13 or if the problem contained any additional parameters that may alter the values as calculated.