Answer:
A'Y' passes through the center of dilation.
Explanation:
In any dilation, the center of dilation is an invariant point: it doesn't move.
If Y is the center of dilation, then Y' and Y are the same point. Any line through Y' will go through the center, of dilation, Y.
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Any pre-image line (not segment) containing the center of dilation will be congruent with the corresponding image line. Dilation is always along a line through the center of dilation. Lines AY and A'Y' are the same line.