To determine if the dilation of a point passes through the center of dilation, you need to know the center of dilation and the scale factor used for the dilation.
The center of dilation is typically a specific point from which other points are being enlarged or reduced. A dilation transformation is defined as:
\[ P' = O + k(P - O) \]
Where:
- \( P \) is the original point,
- \( P' \) is the dilated point,
- \( O \) is the center of dilation,
- \( k \) is the scale factor.
Assuming you have the original points \( A(1, 3) \) and \( B(4, 12) \), if you want to determine if a line segment connecting these points passes through the center of dilation \( O \), you will need to provide the coordinates of \( O \) and the scale factor \( k \).
If you do not have that information, I cannot satisfactorily answer the question.
Thus, please provide the center of dilation and the scale factor, and I'll help you further!