Compare and contrast the effect that reflections, translations, and rotations have on a figure’s shape, size, andorientation.
Question
Compare and contrast the effect that reflections, translations, and rotations have on a figure’s shape, size, and orientation.
Solution
Reflections, translations, and rotations are all transformations that can be applied to a figure in a plane. However, they each have different effects on the figure's shape, size, and orientation.
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Reflections: A reflection is a transformation that flips a figure over a line, creating a mirror image. The size and shape of the figure remain the same, but the orientation changes. For example, if you reflect a right-handed figure, you get a left-handed figure.
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Translations: A translation is a transformation that slides a figure from one place to another without turning it. The size, shape, and orientation of the figure remain the same. Only the position changes.
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Rotations: A rotation is a transformation that turns a figure around a fixed point, called the center of rotation. The size and shape of the figure remain the same, but the orientation changes. The amount of change in orientation depends on the degree of rotation.
In summary, reflections and rotations change the orientation of a figure but not its size or shape. Translations, on the other hand, do not change the size, shape, or orientation of a figure, only its position.
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