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Q: Which property of a rigid transformation is exclusive to rotations? The measures of the angles and sides in the preimage are preserved. A line segment connecting the image to the preimage forms a
90° angle with the center of rotation. The distance from each point on the image to the center of rotation is preserved. All the points on the image move along a parallel line when the preimage is transformed.
A: Answer: A rigid transformation is a geometrical term for the pre-image and the image both having the exact same size and shape. n mathematics, [ a rigid transformation (isometry) of a vector space preserves distances between every pair of points.[1] [2] Rigid transformations of the plane R2, space R3, or real n-dimensional space Rn are termed a Euclidean transformation because they form the
basis of Euclidean geometry.[3] The Rigid transformations include rotations, translations, reflections, or their combination. Sometimes reflections are excluded from the definition of a rigid transformation by imposing that the transformation also preserve the handedness of figures in the Euclidean space (a reflection would not preserve handedness; for instance, it would transform a left hand into a right hand). To avoid ambiguity, this smaller class of transformations is known as proper rigid transformations (informally, also known as roto-translations). In general, any proper rigid transformation can be decomposed as a rotation followed by a translation, while any rigid transformation can be decomposed as an improper rotation followed by a translation (or as a sequence of reflections). Any object will keep the same shape and size after a proper rigid transformation, but not after an improper one. All rigid transformations are affine transformations. Rigid transformations which involve a translation are not linear transformations. Not all transformations are rigid transformations. An example is a shear, which changes two axes in different ways, or a similarity transformation, which preserves angles but not lengths. The set of all (proper and improper) rigid transformations is a group called the Euclidean group, denoted E(n) for n-dimensional Euclidean spaces). The set of proper rigid transformation is called special Euclidean group, denoted SE(n). In mechanics, proper rigid transformations in a 3-dimensional Euclidean space, denoted SE(3), are used to represent the linear and angular displacement of rigid bodies. From Wikipedia, the free encyclopedia ]
Expert answered|marissa-sarol|Points 81|
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Asked 6/19/2013 9:47:44 AM
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