Question

△rst has vertices r(8,2), s(4,1), and t(8,0). △rst has vertices r(24,6), s(12,3), and t(24,0). (a) complete the following. the line through s and t does not pass through the center of d the line through r and s passes through the center of dilation. (b) find each slope below. slope of (overleftrightarrow{st}) = slope of (overleftrightarrow{st}) = slope of (overleftrightarrow{rs}) = slope of (overleftrightarrow{rs}) =

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope of $\overleftrightarrow{ST}$

For points $S(4,1)$ and $T(8,0)$, $m_{ST}=\frac{0 - 1}{8 - 4}=\frac{-1}{4}=-\frac{1}{4}$.

Step3: Calculate slope of $\overleftrightarrow{S'T'}$

For points $S'(12,3)$ and $T'(24,0)$, $m_{S'T'}=\frac{0 - 3}{24 - 12}=\frac{-3}{12}=-\frac{1}{4}$.

Step4: Calculate slope of $\overleftrightarrow{RS}$

For points $R(8,2)$ and $S(4,1)$, $m_{RS}=\frac{1 - 2}{4 - 8}=\frac{-1}{-4}=\frac{1}{4}$.

Step5: Calculate slope of $\overleftrightarrow{R'S'}$

For points $R'(24,6)$ and $S'(12,3)$, $m_{R'S'}=\frac{3 - 6}{12 - 24}=\frac{-3}{-12}=\frac{1}{4}$.

Answer:

slope of $\overleftrightarrow{ST}$ = slope of $\overleftrightarrow{S'T'}=-\frac{1}{4}$
slope of $\overleftrightarrow{RS}$ = slope of $\overleftrightarrow{R'S'}=\frac{1}{4}$