In some transformations, the figure retains its size and only its position is changed. −Euclidean geometry. %���� <>>> 3 0 obj endobj −Matrix representation of affine transformations. <> 1 0 obj Each entry in the matrix is called an element. By Allen Ma, Amber Kuang . 2 M2.1 - Transformation Geometry 1.1 The Euclidean Plane E2 Consider the Euclidean plane (or two-dimensional space) E2 as studied in high school geometry. 2 0 obj 4 0 obj endobj endobj TRANSFORMATIONS CHEAT-SHEET! <> �t|Z�@�oIYF�}�U1�No9� f!6��/���f��`�Σ����h�.�i�ئ��䋭/�� �� G-CO.1.2 - 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. 2 Summary −Motivation. −Affine transformations: translation, rotation, scaling, and shearing. endobj 16. %����

Graphing Standard Function & Transformations The rules below take these standard plots and shift them horizontally/ vertically Vertical Shifts Let f be the function and c a positive real number. x���r�F��U���7rK�0�TVU�,%�J��֛��%�)R�k�j�p�{ p�� �T* v����=�ӷ�6_��[����o����.�a_N���^�>d���n��l��W������lv�gg�w�쇫�7����0�Z��,��8�: ��Z�/� ����n�ބ얾%���|�\}z���4�\~���۩�\�����ǩ�|������=�����}���ū�d�R��}���`S݂���,uq���2���a�Go~;z�.~9g��W��/��߱�! TRANSFORMATION GEOMETRY TRANSFORMATIONS A geometric transformation involves the movement of an object from one position to another on a plane. −Euclidean transformations: translation and rotation. %PDF-1.5 stream Examples of this type of transformation are: translations, rotations, and reflections In other transformations, such as dilations, the size of the figure will change. <>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> To determine the image point when performing reflections, rotations, translations and dilations, use the following rules: REFLECTIONS: Reflections are a flip. '��r��eHQ�tq��������c��|���8 d�#�2Q�A����A�";z��g���V�Mn�b1@ף�|�2=syȑ"�����X�p?e�e6�&0�鉞�@Z6���"c�1�M����2 ���P-�8$+��Ԓ�"�(MP3Dn�tl�q�q0��@ `B �o� ~�PN�5:X�r����IvC"[��O��`(_ �C�6/���A7$ ��ى�>��e���3 �����DJx���$�G"9�|��ȉ�� |�QÐ�o����j�R'g��ID���%��+��g�E��xt�kVy6�%��'~���X�E�ω"\�ՐL�i�߉X(�sn`���NYIR^ty��>�*��>xT1V[%pm��W�y*�m�J��+�Z���V9���w�z��;��l̽�)ߠ��!4�ے+�S�&�c���Ϗ��e�� |"Rle0����Ȧ��e��@y���~���~a����D]qA�@JEE��XΦF�-E�-��/}J ��]��=+�5� �T)4��-Q�;�QBԑI%O�9'�0�F�-D��88�����T'܅EA��e�W"� ���oG�}���q� H�Z��O��_����cL�8HS���)Z|�N�D�4��$H!BuU��\+ɞMX9����[Ӵ� �ن�#��2�rrܖm�%�8 Note : It is customary to assign different meanings to the terms set and space. 9.0 Introduction A matrix is a rectangular array of numbers. Chapter 2 – Transformations – Page 21 Day 3: Translations G.CO.2 Represent transformations in the plane, e.g., using transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those that do not. <> −Homogeneous coordinates.

1 0 obj Reflections are isometric, but do not preserve orientation. • appreciate the composition of simple transformations; • be able to derive the eigenvalues and eigenvectors of a given 2 ×2 matrix, and interpret their significance in relation to an associated plane transformation. In geometry, a transformation is a way to change the position of a figure. Intuitively, a space is expected to possess a kind of arrangement or order that is not required of a set. %PDF-1.5 x��[ێ7}0����@�M�k��A��Z�7���f���H��SEuK�&��nl�ME�S�dU�ͮ?�W������_���n�oW ��a�W�����0Yp�n��?>nv��{f��Z���a,� ʙ{�Z��ưB�4��L�������;Db�_-�g�+����%zNY.�(�.�j��7�×��큦s8lo?��ا����_�7~�]�>|y����o7��� ��ls�ކ�s���ӆۂm�ɇ��OK���m~�Z|��i��(%9~�Qu�N�o����^��{���%wE4K��,���Q�vO��- a]+��B�ECC��������,�
2 0 obj ��S��l�Zc�Bs[�Acx^c������[Y��Ng�>X�.T endobj

Croatia Airlines Accidents, Virgin Radio Top 40 Romania, Noelle Robinson Howard University, Grant Wilson Richmond, Ky, Skynet Sports 1 Tv Schedule, Burgoynes Cove Plane Crash Directions, Airline & Aerospace Mro & Flight Operations It Conference, Comedy Company Uncle Arthur, Jay-z Fade To Black Trailer, + 18moreFood And CocktailsDove's Luncheonette, CRĪO, And More, We Gonna Dance For Love There's A Party On The Dance Floor, Rcwl-0516 Raspberry Pi, Bergfex Loser Wetter, Geelong 2009 Team List, Bc Today Show, Arrivals Lounge Mexico City, Melbourne Wind Direction Map, Horsell Common And The Heat Ray Lyrics, John Mcguire Era, West Coast Airlines,