Answer:
D
Step-by-step explanation:
Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2).
Consider option A.
1st transformation [tex](x+0,y-2)[/tex] will map vertices of the square into points
- [tex](2,1)\rightarrow (2,-1);[/tex]
- [tex](1,2)\rightarrow (1,0);[/tex]
- [tex](2,3)\rightarrow (2,1);[/tex]
- [tex](3,2)\rightarrow (3,0).[/tex]
2nd transformation = reflection over y = 1 has the rule (x,2-y). So,
- [tex](2,-1)\rightarrow (2,3);[/tex]
- [tex](1,0)\rightarrow (1,2);[/tex]
- [tex](2,1)\rightarrow (2,1);[/tex]
- [tex](3,0)\rightarrow (3,2)[/tex]
These points are exactly the vertices of the initial square.
Consider option B.
1st transformation [tex](x+2,y-0)[/tex] will map vertices of the square into points
- [tex](2,1)\rightarrow (4,1);[/tex]
- [tex](1,2)\rightarrow (3,2);[/tex]
- [tex](2,3)\rightarrow (4,3);[/tex]
- [tex](3,2)\rightarrow (5,2).[/tex]
2nd transformation = reflection over x = 3 has the rule (6-x,y). So,
- [tex](4,1)\rightarrow (2,1);[/tex]
- [tex](3,2)\rightarrow (3,2);[/tex]
- [tex](4,3)\rightarrow (2,3);[/tex]
- [tex](5,2)\rightarrow (1,2)[/tex]
These points are exactly the vertices of the initial square.
Consider option C.
1st transformation [tex](x+3,y+3)[/tex] will map vertices of the square into points
- [tex](2,1)\rightarrow (5,4);[/tex]
- [tex](1,2)\rightarrow (4,5);[/tex]
- [tex](2,3)\rightarrow (5,6);[/tex]
- [tex](3,2)\rightarrow (6,5).[/tex]
2nd transformation = reflection over y = -x + 7 will map vertices into points
- [tex](5,4)\rightarrow (3,2);[/tex]
- [tex](4,5)\rightarrow (2,3);[/tex]
- [tex](5,6)\rightarrow (1,2);[/tex]
- [tex](6,5)\rightarrow (2,1)[/tex]
These points are exactly the vertices of the initial square.
Consider option D.
1st transformation [tex](x-3,y-3)[/tex] will map vertices of the square into points
- [tex](2,1)\rightarrow (-1,-2);[/tex]
- [tex](1,2)\rightarrow (-2,-1);[/tex]
- [tex](2,3)\rightarrow (-1,0);[/tex]
- [tex](3,2)\rightarrow (0,-1).[/tex]
2nd transformation = reflection over y = -x + 2 will map vertices into points
- [tex](-1,-2)\rightarrow (4,3);[/tex]
- [tex](-2,-1)\rightarrow (3,4);[/tex]
- [tex](-1,0)\rightarrow (2,3);[/tex]
- [tex](0,-1)\rightarrow (3,2)[/tex]
These points are not the vertices of the initial square.
