To solve for \( y \), the distance between points \( R \) and \( R' \) when segment \( QR \) is dilated to create segment \( Q'R' \) using the dilation rule \( D_{T, 1.5} \), we first interpret the dilation rule.
The rule \( D_{T, 1.5} \) indicates that every point is moved away from the center of dilation \( T \) by a factor of 1.5. This means that the distance from point \( T \) to point \( R \) will be multiplied by 1.5 to determine the distance from \( T \) to point \( R' \).
Given that the length of \( RT \) is 6, we can find the length of \( R'T \) using the dilation factor:
\[ R'T = 1.5 \times RT = 1.5 \times 6 = 9. \]
Now, we can find \( y \), the distance between \( R \) and \( R' \):
\[ y = R'T - RT = 9 - 6 = 3. \]
Thus, the distance between points \( R \) and \( R' \) is
\[ \boxed{3} \text{ units}. \]
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