Math Problem Statement
Solution
The question asks which of the given rotations will map the polygon onto itself. The polygon shown is a square, as indicated by its four equal sides and right angles.
For a square, rotations that map it onto itself (known as symmetries) must be multiples of because it has four symmetrical positions (0°, 90°, 180°, and 270°).
Let's examine each option:
- Rotation of 45° clockwise: This does not map the square onto itself, as 45° is not a multiple of 90°.
- Rotation of 90° counterclockwise: This does map the square onto itself because 90° is one of the symmetrical rotations.
- Rotation of 120° counterclockwise: This does not map the square onto itself, as 120° is not a multiple of 90°.
- Rotation of 30° counterclockwise: This does not map the square onto itself, as 30° is not a multiple of 90°.
So, only the 90° rotation (option 2) will carry the square onto itself.
Would you like a more detailed explanation or have any questions?
Here are some additional related questions to explore:
- What are the rotational symmetries of other regular polygons, like a hexagon?
- How can we identify the angle of rotation symmetry for any regular polygon?
- What other types of transformations can map a square onto itself?
- What is the relationship between the number of sides of a regular polygon and its angle of rotation symmetry?
- How do rotational and reflectional symmetries differ in polygons?
Tip: For a regular polygon with sides, the smallest angle of rotation symmetry is .
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Math Problem Analysis
Mathematical Concepts
Geometry
Symmetry
Rotational Symmetry
Formulas
Angle of rotation symmetry for a regular polygon = 360° / n
Theorems
Symmetry Theorem for Regular Polygons
Suitable Grade Level
Grades 7-9
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