Question

Line segment QR is dilated to create line segment Q'R' using the dilation rule DT,1.5.

Point T is the center of dilation. Line segment Q R is dilated to create line segment Q prime R prime. The length of R T is 6 and the length of R prime R is y.

What is y, the distance between points R and R'?

3 units
4 units
6 units
9 units

Answer 1

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

\[
\boxed{3} \text{ units}.
\]