Which of the following rotation operations are involutory? Match the rotation operations that achieve the same outcome.
Understand the Problem
The question is asking which rotation operations are involutory and requires matching various rotation operations to achieve the same outcome. It involves understanding properties of geometric transformations.
Answer
Rotate 180°, flip left-right, flip up-down, transpose are involutory.
Rotation operations that are involutory include rotate 180°, flip left-right, flip up-down, and transpose. For matching operations: transpose corresponds to flip left-right then rotate -90°; anti-diagonal transpose corresponds to rotate +90° then flip left-right; rotate 180° corresponds to flip left-right then flip left-right; flip up-down then flip up-down corresponds to flip left-right then flip up-down.
Answer for screen readers
Rotation operations that are involutory include rotate 180°, flip left-right, flip up-down, and transpose. For matching operations: transpose corresponds to flip left-right then rotate -90°; anti-diagonal transpose corresponds to rotate +90° then flip left-right; rotate 180° corresponds to flip left-right then flip left-right; flip up-down then flip up-down corresponds to flip left-right then flip up-down.
More Information
Involutory operations include any transformations that return to the original state upon performing twice such as rotations of 180° or full flips over an axis.
Tips
Ensure to check that performing the operation twice results in the original state when determining involutory operations.
Sources
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