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REFLECTIONS: Reflections are a flip. 0000006686 00000 n
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Ø The "prime notation is used to represent a transformed figure of the original figure. 0000003289 00000 n
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Standard: MGSE9–12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. 0000005083 00000 n
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h�bbd``b`i�E@���X�A�( �V{$D �H��4 ���4���5�� The notion of inversion, or reflection in a circle, is the key tool employed. Ø A pre-figure or pre-image is the original object. • Rigid transformation: translation and rotation only • A coordinate frame can also be written as an homogenous matrix • Frames and rigid body transformations are equivalent – they correspond to a geometric and algebraic view – columns of the rotation matrix are the axes of a coord. 0000007524 00000 n
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16 − Set of geometric transformations: translations and rotations (also called isometries). The study of algebraic curves, which started with the study of conic sections, developed into algebraic geome-try. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry).
What is transformation? − By using homogeneous coordinates, these transformations can be represented through matrices 3x3. 0000002225 00000 n
Introduction If you had a lump of clay and wanted to make a bowl, you would most likely fashion the clay by
Geometric Transformation CS 211A. The Mathematics of Graphical Transformations: Vector Geometric and Coordinate-Based Approaches Page 1 DesignLab Technical Report DL-1997-03 J. R. Miller January 1997 (Rev: 4/22/08) I. Reflections are isometric, but do not preserve orientation.
Ø In geometry, transformations refer to the _____ of objects on a coordinate plane. iv M2.1 - Transformation Geometry tion.
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Consider the graph below, circle the pre-image and box the transformed image. Homogeneous Coordinates 0000002141 00000 n
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The reexamination of the system of axioms of Euclid’s Elements led to David Hilbert’s (1862-1943) foundations of geometry and to axiomatic tendency of present day mathematics. geometric transformations and to determine the potential opportunity to learn transformation concepts as measured by textbook physical characteristics, lesson narratives, and analysis of student exercises with level of cognitive demand.
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