 # Rigid Motion in a Plane 7.1.

## Presentation on theme: "Rigid Motion in a Plane 7.1."— Presentation transcript:

Rigid Motion in a Plane 7.1

Liberty Lancers Transformations
A operation that maps, or moves, a preimage onto an image. Liberty Lancers

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?

Types of Transformations
Translation Reflection Rotation Each link will go to NLVM demonstration of the transformation.

Image and Preimage Preimage: 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.

Notations Notation for transformations is A A’ In your Homework
We read this as A maps to A’ In your Homework Naming a transformation is naming the image that results (for HW problems) Describing a transformation is telling what kind it is

Try this on your own. 1. 2. 3. 4. 5.

Reflections and Symmetry
7.2

Reflections A type of transformation that uses a line that acts like a mirror, with an image reflected over the line.

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

Types of symmetry Bilateral (reflectional) symmetry: when a form has equal mirror images on both sides of a line or plane. Horizontal Vertical Rotational symmetry: when a form has equal mirror images after rotating it around a center point.

What types of symmetry do the letters of your name have?

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.

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.

Reflection on the y-axis
This is true for any figure! Measurements stay the same Each point is the same distance from the line of reflection as its image Only orientation (the order of the points) changes

Reflections on the x-axis
ALWAYS changes the y coordinate (x,y) (x,-y) B(5,1) B’(5,-1)

Reflections on y=x Each (x,y) coordinate gets reversed (x,y) (y,x)
All measurements are the same Orientation still changes.

Questions Can you tell how many lines of symmetry each figure has? State how many each shape has, if any.

Questions

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, 35 7.2 - Pg. 406: 18-29, 48-49