Question

that $\triangle rst$ has vertices $r(9,6)$, $s(15,15)$, and $t(18,12)$. note that $\triangle rst$ has vertices $r(3,2)$, $s(5,5)$, and $t(6,4)$.
(a) complete the following.
the line through $r$ and $s$ passes through the center of dilation.
the line through $r$ and $t$ does not pass through the center of dilation.
(b) find each slope below.
slope of $overrightarrow{rs}$ = slope of $overrightarrow{rs}$ =
slope of $overrightarrow{rt}$ = slope of $overrightarrow{rt}$ =

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope of $\overrightarrow{RS}$

For points $R(9,6)$ and $S(15,15)$, $m_{RS}=\frac{15 - 6}{15 - 9}=\frac{9}{6}=\frac{3}{2}$.

Step3: Calculate slope of $\overrightarrow{R'S'}$

For points $R'(3,2)$ and $S'(5,5)$, $m_{R'S'}=\frac{5 - 2}{5 - 3}=\frac{3}{2}$.

Step4: Calculate slope of $\overrightarrow{RT}$

For points $R(9,6)$ and $T(18,12)$, $m_{RT}=\frac{12 - 6}{18 - 9}=\frac{6}{9}=\frac{2}{3}$.

Step5: Calculate slope of $\overrightarrow{R'T'}$

For points $R'(3,2)$ and $T'(6,4)$, $m_{R'T'}=\frac{4 - 2}{6 - 3}=\frac{2}{3}$.

Answer:

slope of $\overrightarrow{RS}$ = slope of $\overrightarrow{R'S'}=\frac{3}{2}$
slope of $\overrightarrow{RT}$ = slope of $\overrightarrow{R'T'}=\frac{2}{3}$