Disclaimer: this study guide was not created to replace Geometry your textbook and is for classroom or individual use only. is used to is used Study Guides Study Page 1 of 2 Page A’
ions are special cases. A ). ). ). ). t . ). ). A’ x, y x, -y y = -x b - y y, x b - y 2 2 -x, -y x, x, and , primes are used to label the image. The arrow arrow The image. to label the used are , primes y = x image x and the and , then the image is ( =- (or congruence transformations) transform a figure without changing its size or -coordinates change y , then the image is ( y , then the image is ( , then the image is ( -axis, then the image is ( -axis, -axis, then the image is (- -axis, , then the image would be y = x y x A ransforma -coordinates stay constant -coordinates stay and y = -x y = b y = b y preimage x T = y of transformations
: An operation that moves, flips, or changes a figure to create a new figure. flips, or changes a figure to create a that moves, : An operation
: A transformation that does not preserve size. that does not preserve : A transformation : Another word for rigid transformation, a transformation that does not change the shape or size of a This guide was created by Nicole Crawford, Jane Li, Amy Shen, and Zachary Shen, and Zachary Jane Li, Amy Nicole Crawford, created by This guide was learn more about the student authors, http://www.ck12.org/about/ Wilson. To ck-12-interns/. rigid : The original figure before a transformation. : The original figure ) is reflected over the over ) is reflected over ) is reflected ) is reflected over the over ) is reflected ) is reflected over the over ) is reflected ) is reflected over over ) is reflected ) is reflected over over ) is reflected : A transformation that preserves size and shape. size that preserves : A transformation figure. : A quantity that has direction and size. that : A quantity : The figure after a transformation. : The figure after a x, y x, y x, y x, y x, y x, y ypes Rigid Isometry Non-Rigid If ( If ( If ( Image is the same distance away from the reflection line as the preimage. Image is the same distance away If ( If ( If ( Example: If the preimage is Reflection: A transformation that turns a figure into its mirror image by flipping it over a line. by flipping it mirror image that turns a figure into its A transformation Reflection: point to create an image. that turns a figure around a fixed A transformation Rotation: distance in the same direction. point in a figure the same every that moves transformation A Translation: Reflections Rigid Transformations Big Picture Key Terms • • • • • • • • • • • -coordinates change while -coordinates stay the same while -coordinates stay Reflections over line can be a line of reflection, but the lines Any x Reflection Over Vertical Lines Reflection Over Horizontal Lines Reflection Over Horizontal x To distinguish between the distinguish the between To describe a transformation. to describe a reflection is a “flip.” Another way The three types of rigid transformations are: of rigid transformations The three types Image Vector Specifically, shape. Transformation Preimage Transformations move and modify geometric shapes. There are several types of transformations that all transform all transform that transformations of types several are There shapes. geometric modify and move Transformations or non-rigid. can be rigid (isometric) These transformations ways. different figures in T Geometry T Page 2of 2 Vectors Rotation of270° Rotation of180° Rotation of90° Same asa“reflectionintheorigin,” afigureisspunaroundtheorigin. then thepreimage isrotatedaround180°about thecenterofdilation. transformationtransformsnon-rigid ( a plane, coordinate a In A dilationisa The translation ruleforthisfigureis:( where the point ( ( notation: the by described be can translation A Translations intheCoordinatePlane • • • • • • • • • • • • • Translations Rotations Dilations The vector forthistranslation is<6,-4>. Always produc Reduction orcontraction: 0
x, y e asimilarshapetotheoriginal of ) is translated horizontally T A to ransforma B islabeled x, y ) that preserves shapebutnotsize. AB a ( unitsand vertically . x + x, y A is the initial point and isthe initial 6 AB ) ) , y+ is<3,7>. ( 4). x + a, y + b x, y t ions ) ) b units. y, x y, -x x, -y ( kx, ky ). ), B ). ).
), where ), con k is the scale factor. If t . k < 0 ,