Question and answer
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.
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|
Question
Asked 6/19/2013 9:47:44 AM
0 Answers/Comments
Get an answer
New answers
Rating

There are no new answers.

Comments

There are no comments.

Add an answer or comment
Log in or sign up first.
0 questions answered
Popular Conversations
In the poem "God's Grandeur," the phrase "nor can foot feel, being ...
Weegy: In the poem "God's Grandeur," the phrase "nor can foot feel, being shod" means: humans are out of touch with ...
11/27/2014 12:04:03 AM| 1 Answers
Weegy Stuff
S
L
1
L
P
C
1
P
C
1
L
P
C
1
Points 2859 [Total 14569]| Ratings 10| Comments 2759| Invitations 0|Online
S
L
Points 1472 [Total 3758]| Ratings 0| Comments 1472| Invitations 0|Offline
S
Points 835 [Total 867]| Ratings 1| Comments 825| Invitations 0|Offline
S
L
Points 777 [Total 1298]| Ratings 6| Comments 717| Invitations 0|Offline
S
1
L
1
L
P
P
L
P
Points 773 [Total 14147]| Ratings 0| Comments 773| Invitations 0|Offline
S
1
L
L
Points 273 [Total 6667]| Ratings 0| Comments 273| Invitations 0|Offline
S
L
Points 162 [Total 1458]| Ratings 3| Comments 132| Invitations 0|Offline
S
Points 102 [Total 102]| Ratings 1| Comments 92| Invitations 0|Offline
S
Points 50 [Total 50]| Ratings 0| Comments 0| Invitations 5|Offline
S
Points 46 [Total 46]| Ratings 3| Comments 6| Invitations 1|Offline
Home | Contact | Blog | About | Terms | Privacy | Social | ©2014 Purple Inc.