Answer:
[tex](x,y)\rightarrow (x, y-7)\text{ and reflected across x = 4}[/tex]
Step-by-step explanation:
∵ The rule of reflection across x = 4,
[tex](x,y)\rightarrow (8-x,y)[/tex]
Rule of reflection across y = 4
[tex](x,y)\rightarrow (x, 8-y)[/tex]
Rule of reflection across x = 0
[tex](x,y)\rightarrow (-x,y)[/tex]
Thus, [tex](x,y)\rightarrow (x, y-7)\text{ and reflected across x = 4}[/tex]
[tex]\implies (x,y)\rightarrow (x,y-7)\rightarrow (8-x, y-7)[/tex]
[tex](x,y)\rightarrow (x-3, y)\text{ and reflected across x = 4}[/tex]
[tex]\implies (x,y)\rightarrow (x-3,y)\rightarrow (11-x, y)[/tex]
[tex](x,y)\rightarrow (x-3, y)\text{ and reflected across y = 4}[/tex]
[tex]\implies (x,y)\rightarrow (x-3,y)\rightarrow (x-3, 8-y)[/tex]
[tex](x,y)\rightarrow (x, y-7)\text{ and reflected across x = 0}[/tex]
[tex]\implies (x,y)\rightarrow (x,y-7)\rightarrow (-x, y-7)[/tex]
Here, the coordinates of triangle ABC are,
A ≡ (3, 3), B≡(7,6), C≡(7,2)
And, the coordinates of transformed triangle,
D ≡ (5,-4) E≡(1,-1), F≡(1,-5)
Therefore, by the above explanation,
The glide reflection that shows the mapping [tex]\triangle ABC\rightarrow \triangle D EF[/tex] is,
[tex](x,y)\rightarrow (x, y-7)\text{ and reflected across x = 4}[/tex]
