To solve these rotation problems, we use rotation formulas:

Rotation Formulas:

1. 270° Counterclockwise Rotation:
   The formula for a 270° counterclockwise rotation around the origin is: $(x, y) \to (y, -x)$

2. 180° Counterclockwise Rotation:
   The formula for a 180° counterclockwise rotation around the origin is: $(x, y) \to (-x, -y)$

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1. Rhombus CDEF - 270° Counterclockwise

Vertices:

• C(-5, 5):
  $(-5, 5) \to (5, 5)$
• D(-1, 7):
  $(-1, 7) \to (7, 1)$
• E(-3, 3):
  $(-3, 3) \to (3, 3)$
• F(-7, 1):
  $(-7, 1) \to (1, 7)$

New vertices:

• $C'(5, 5)$
• $D'(7, 1)$
• $E'(3, 3)$
• $F'(1, 7)$

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2. Rectangle WXYZ - 180° Counterclockwise

Vertices:

• W(-3, -5):
  $(-3, -5) \to (3, 5)$
• X(1, -1):
  $(1, -1) \to (-1, 1)$
• Y(3, -3):
  $(3, -3) \to (-3, 3)$
• Z(-1, -7):
  $(-1, -7) \to (1, 7)$

New vertices:

• $W'(3, 5)$
• $X'(-1, 1)$
• $Y'(-3, 3)$
• $Z'(1, 7)$

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Final Answer:

1. Rhombus CDEF (270° Counterclockwise)

• $C'(5, 5)$
• $D'(7, 1)$
• $E'(3, 3)$
• $F'(1, 7)$

2. Rectangle WXYZ (180° Counterclockwise)

• $W'(3, 5)$
• $X'(-1, 1)$
• $Y'(-3, 3)$
• $Z'(1, 7)$

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Do you want detailed steps for the transformations or have any other questions?

Expanding questions:

1. What happens if we rotate by 90° counterclockwise instead?
2. How do the coordinates change for a 360° rotation?
3. What is the general rule for rotation about a different center?
4. How can you verify rotations on a graph?
5. How does rotation affect the shape's area and orientation?

Tip: Always sketch the points on graph paper for visual verification of your transformations.