(4,4)
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To find the image of a point after a dilation, we multiply the coordinates of the point by the scale factor.
In this case, the scale factor is 1/3.
So, to find the image of (12,12), we multiply each coordinate by 1/3:
- (12*(1/3), 12*(1/3)) = (4,4)
Therefore, the image of (12,12) after a dilation by a scale factor of 1/3 centered at the origin is (4,4).