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Since the scale factor is 13 and the center of dilation is the origin, we can find the coordinates of A' and B' by multiplying the coordinates of A and B by the scale factor.
A' = (-6 * 13, 3 * 13) = (-78, 39)
B' = (-12 * 13, 9 * 13) = (-156, 117)
Therefore, the coordinates of A' and B' are A'(-78, 39) and B'(-156, 117).