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.
21,971,524 questions answered
Popular Conversations
mesosphere
Weegy: Stratospher is between the troposphere and the mesosphere in earths atmosphere. User: stratosphere User: ...
9/1/2015 5:07:52 PM| 4 Answers
The etymology of a word is sometimes reflected in its ...
Weegy: Have a great day! Ask Weegy again soon User: The transition word(s) that would best introduce an example ...
8/31/2015 6:25:44 AM| 2 Answers
Find the value of 83 - [59 - (22 - 18)].
Weegy: 83 - (59 - (22 - 18)) =83 - (59 - 4) =83 - 55 =28 User: Find the value of 5 · 2 ^3
8/31/2015 8:28:09 AM| 2 Answers
Find two consecutive integers whose sum is 67. Which of the ...
Weegy: To find two consecutive integers whose sum is 67 use the equation 2x + 1= 67 2x + 1= 67 2x = 67 - 1 2x = ...
8/31/2015 9:51:16 AM| 2 Answers
Weegy Stuff
S
1
L
L
P
R
Points 27 [Total 9350]| Ratings 0| Comments 27| Invitations 0|Online
S
L
L
P
1
Points 27 [Total 9337]| Ratings 1| Comments 17| Invitations 0|Offline
S
Points 25 [Total 809]| Ratings 0| Comments 25| Invitations 0|Offline
S
Points 21 [Total 326]| Ratings 0| Comments 21| Invitations 0|Offline
S
Points 9 [Total 197]| Ratings 0| Comments 9| Invitations 0|Offline
S
Points 9 [Total 233]| Ratings 0| Comments 9| Invitations 0|Offline
Points 0 [Total 0]| Ratings 0| Comments 0| Invitations 0|Offline
Points 0 [Total 0]| Ratings 0| Comments 0| Invitations 0|Offline
S
Points 0 [Total 0]| Ratings 0| Comments 0| Invitations 0|Offline
S
Points 0 [Total 0]| Ratings 0| Comments 0| Invitations 0|Offline
Home | Contact | Blog | About | Terms | Privacy | Social | ©2015 Purple Inc.