Which series of transformations will not map figure H onto itself

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RenderVanez RenderVanez

03-11-2019
Mathematics

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Which series of transformations will not map figure H onto itself

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frika frika · Answer 1 · 2019-11-07T23:12:16+01:00

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.

Millanamarie Millanamarie · Answer 2 · 2020-11-27T19:08:08+01:00

Millanamarie Millanamarie

27-11-2020

Answer:

D

Step-by-step explanation:

I took the test , it was correct.

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