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

Question

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 $R^{\prime }$ when segment $QR$ is dilated to create segment $Q^{\prime }{R}^{\prime }$ 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 $R^{\prime }$.

Given that the length of $RT$ is 6, we can find the length of $R^{\prime }T$ using the dilation factor:

$$R^{\prime }T=1.5\times RT=1.5\times 6=9.$$

Now, we can find $y$, the distance between $R$ and $R^{\prime }$:

$$y=R^{\prime }T-RT=9-6=3.$$

Thus, the distance between points $R$ and $R^{\prime }$ is

$$\boxed{{\displaystyle 3}}\text{ units}.$$