Question

in exercises 17 and 19, graph $\triangle rst$ with vertices $r(4, 1), s(7, 3),$ and $t(6, 4)$ and its image after the glide reflection.

1. translation: $(x,y) \

ightarrow (x,y - 1)$
reflection: in the $y$-axis

1. translation: $(x,y) \

ightarrow (x,y + 4)$
reflection: in the line $x = 3$

Explanation:

For Exercise 17:

Step1: Apply translation to vertices

For $R(4,1)$: $(4, 1-1)=(4,0)$
For $S(7,3)$: $(7, 3-1)=(7,2)$
For $T(6,4)$: $(6, 4-1)=(6,3)$

Step2: Reflect over y-axis

Rule: $(x,y)\to(-x,y)$
For $(4,0)$: $(-4,0)$
For $(7,2)$: $(-7,2)$
For $(6,3)$: $(-6,3)$

Step1: Apply translation to vertices

For $R(4,1)$: $(4, 1+4)=(4,5)$
For $S(7,3)$: $(7, 3+4)=(7,7)$
For $T(6,4)$: $(6, 4+4)=(6,8)$

Step2: Reflect over $x=3$

Rule: $(x,y)\to(2\times3 - x,y)=(6-x,y)$
For $(4,5)$: $(6-4,5)=(2,5)$
For $(7,7)$: $(6-7,7)=(-1,7)$
For $(6,8)$: $(6-6,8)=(0,8)$

Answer:

Original vertices: $R(4,1)$, $S(7,3)$, $T(6,4)$
Translated vertices: $R'(4,0)$, $S'(7,2)$, $T'(6,3)$
Final image vertices: $R''(-4,0)$, $S''(-7,2)$, $T''(-6,3)$

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For Exercise 19: