rigid motion in a plane 7.1. transformations a operation that maps, or moves, a preimage onto an...

Rigid Motion in a Plane 7.1

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?

Types of Transformations Translation Reflection Rotation

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.

Notations Notation for transformations is A A’

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

4

2

-2

-4

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Image

PreimageD' C'

B'A'

D C

BA

Try this on your own.

1.2.3.4.5.

Reflections and Symmetry7.2

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.

In your notes Write down your name in large

uppercase letters.

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

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2

-2

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JI

H

G

F

E

D

BC

A

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

4

2

-2

-4

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A'

B' C' C B

A 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)

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2

-2

-4

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A'

C' B'

C B

A

Reflections on y=x Each (x,y)

coordinate gets reversed

(x,y) (y,x) All measurements

are the same Orientation still

changes.

4

2

-2

-4

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C'

B'

A'

CB

A

f x = x

Questions Can you tell how many lines of symmetry

each figure has? State how many each shape has, if any.

Questions

Exit Ticket Homework 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