2 Liberty Lancers Transformations A operation that maps, or moves, a preimage onto an image.Liberty Lancers
3 Isometry A transformation that preserves lengths (also called a rigid transformation)How can I change this shape’s appearance without changing it’s dimensions?I had the students draw a picture on patty paper and gave them coordinate plane white boards. We put the patty paper on top of the grid and performed all the transformations and ask the question… is it an isometry?
4 Types of Transformations TranslationReflectionRotationEach link will go to NLVM demonstration of the transformation.
5 Image and PreimagePreimage: the original figure in a transformation of a figure in a plane.Image: a new figure that results from the transformation of a figure in a plane.
6 Notations Notation for transformations is A A’ In your Homework We read this as A maps to A’In your HomeworkNaming a transformation is naming the image that results (for HW problems)Describing a transformation is telling what kind it is
10 ReflectionsA type of transformation that uses a line that acts like a mirror, with an image reflected over the line.
11 Symmetry: A quality in which a transformation results in an identical form. In order to better understand reflections, we first need to understand the concept of symmetry
12 Types of symmetryBilateral (reflectional) symmetry: when a form has equal mirror images on both sides of a line or plane.HorizontalVerticalRotational symmetry: when a form has equal mirror images after rotating it around a center point.
13 In your notes Write down your name in large uppercase letters. What types of symmetry do the letters of your name have?
14 Reflections Reflections always have symmetry The line that causes symmetry between the two figures is called a line of symmetry.In a reflection, this mirror line is called a line of reflection.
15 Reflection on the y-axis A y-axis reflection always changes the x coordinate for every point. (x,y) (-x,y)G (-2,0) is the exact image of E (2,0) on the other side of the y-axis.
16 Reflection on the y-axis This is true for any figure!Measurements stay the sameEach point is the same distance from the line of reflection as its imageOnly orientation (the order of the points) changes
17 Reflections on the x-axis ALWAYS changes the y coordinate(x,y) (x,-y)B(5,1) B’(5,-1)
18 Reflections on y=x Each (x,y) coordinate gets reversed (x,y) (y,x) All measurements are the sameOrientation still changes.
19 QuestionsCan you tell how many lines of symmetry each figure has? State how many each shape has, if any.
21 Exit Ticket Homework 7.1 - Pg. 399: 12-17, 21, 22, 26-31, 34, 35 On a separate sheet of paper.Describe the difference between a translation, reflection and rotation. Draw a preimage and image of each transformation.7.1 - Pg. 399: 12-17, 21, 22, 26-31, 34, 357.2 - Pg. 406: 18-29, 48-49