QQuestionMathematics
QuestionMathematics
"Explain how a 90 -degree clockwise rotation of a figure is the same as rotating 270 degrees counterclockwise. Be specific and use 2 - 3 sentences (or more).
A 90 -degree clockwise rotation and a 270 -degree counterclockwise rotation result in the same final orientation of a figure. This is because rotating 90 degrees clockwise is equivalent to moving 90 degrees forward, while rotating 270 degrees counterclockwise is equivalent to moving 360 - 270 = 90 degrees backward. Both rotations thus place the figure in the same position relative to its original orientation."
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Answer
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Step 1:: Understand the concept of rotational symmetry
Rotational symmetry refers to the property of a figure that remains unchanged upon rotation around a fixed point. In this case, we are considering a 90 -degree clockwise rotation and a 270 -degree counterclockwise rotation.
Step 2:: Analyze the rotational angles
A 90 -degree clockwise rotation (indicated as CW^90) can be seen as moving 90 degrees forward from the initial position. On the other hand, a 270 -degree counterclockwise rotation (indicated as CCW^270) can be seen as moving 360 - 270 = 90 degrees backward from the initial position.
Step 3:: Compare the final orientations
Since both rotations result in moving 90 degrees from the initial position, the figures will end up in the same orientation after either rotation.
Final Answer
A 90 -degree clockwise rotation and a 270 -degree counterclockwise rotation are equivalent since they both result in moving 90 degrees from the initial position, leading to the same final orientation of the figure.
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