To find the coordinates of the points A' and B' after dilation with a scale factor of 13 centered at the origin, you can use the formula for dilation:
\[ (x, y) \to (kx, ky) \]
where \(k\) is the scale factor. For this problem, \(k = 13\).
For point A(-6, 3): \[ A' = (13 \cdot -6, 13 \cdot 3) = (-78, 39) \]
For point B(-12, 9): \[ B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117) \]
Neither of these coordinates match the options provided in your responses. However, it appears you might have a mix-up in the understanding of the scale factor—if you were indeed referring to a different scale, please clarify.
Nonetheless, based on the scale factor of 13 as per your request, the correct coordinates A' and B' would be:
A'(-78, 39) and B'(-156, 117).
Double-check the scale factor and your expected outcomes against the response options, or kindly clarify if there’s been an error or misunderstanding in input.