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Part 2: Graph the polygon with the given vertices and its image after the transformation. Label all vertices in both the preimage and image using the correct notation.

4. A(2, 1), B(3, -1), C(4, 2), D(3, 3)
Reflection : in the line x = -1

5. A(2, 3), B(1, 4), C(3, 4)
Rotation: 180° about the origin

6. A(5, -2), B(5, 2), C(3, 1), D(2, -1)
Rotation: 270° about the origin

Respuesta :

Answer:

I'm sorry, I can provide the formulas and the steps to graph the polygon and its image, but I am not able to graph the figures.

The preimage of the polygon with vertices A(2,1), B(3,-1), C(4,2), D(3,3) will be reflected in the line x = -1, thus the image will have vertices A'(-2,1), B'(-3,-1), C'(-4,2), D'(-3,3).

The preimage of the polygon with vertices A(2,3), B(1,4), C(3,4) will be rotated 180° about the origin, thus the image will have vertices A'(-2,-3), B'(-1,-4), C'(-3,-4).

The preimage of the polygon with vertices A(5, -2), B(5, 2), C(3, 1), D(2, -1) will be rotated 270° about the origin, thus the image will have vertices A'(2,5), B'(-2,5), C'(-1,3), D'(1,2).

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Answer:

Question 4:

  • A' (-4, 1)
  • B' (-4, -1)
  • C' (-6, 2)
  • D' (-5, 3)

Question 5:

  • A' (-2, -3)
  • B' (-1, -4)
  • C' (-3, -4)

Question 6:

  • A' (-2, -5)
  • B' (2, -5)
  • C' (1, -3)
  • D' (-1, -2)

Step-by-step explanation:

Question 4

Given vertices of the pre-image:

  • A = (2, 1)
  • B = (2, -1)
  • C = (4, 2)
  • D = (3, 3)

If the pre-image is reflected in the line x = -1, the transformation rule is:

  • [tex](x, y) \rightarrow (x-2(x+1), y)[/tex]

Therefore the vertices of the image are:

  • A' = (2 - 2(2 + 1), 1) = (-4, 1)
  • B' = (2 - 2(2 + 1), -1) = (-4, -1)
  • C' = (4 - 2(2 + 1), 2) = (-6, 2)
  • D' = (3 - 2(2 + 1), 3) = (-5, 3)

Question 5

Given vertices of the pre-image:

  • A = (2, 3)
  • B = (1, 4)
  • C = (3, 4)

If the pre-image is rotated 180° about the origin, the transformation rule is:

  • [tex](x, y) \rightarrow (-x,-y)[/tex]

Therefore the vertices of the image are:

  • A' = (-2, -3)
  • B' = (-1, -4)
  • C' = (-3, -4)

Question 6

Given vertices of the pre-image:

  • A = (5, -2)
  • B = (5, 2)
  • C = (3, 1)
  • D = (2, -1)

If the pre-image is rotated 270° about the origin, the transformation rule is:

  • [tex](x, y) \rightarrow (y,-x)[/tex]

If the direction of a rotation is not specified, then it is counterclockwise.

Therefore the vertices of the image are:

  • A' = (-2, -5)
  • B' = (2, -5)
  • C' = (1, -3)
  • D' = (-1, -2)
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