1.2: Transformations

G-CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G-CO.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. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

CCSS

Pre imagePre imageOriginal shape or Original shape or

object.object.

ImageImageShape or object Shape or object after it has been after it has been

moved.moved.

AA

(read as A prime)

TransformationTransformationDefinitionDefinition – anything that maps (or moves) a – anything that maps (or moves) a

pre image to an image.pre image to an image.

4 Basic types of transformations:4 Basic types of transformations:1. Reflection1. Reflection2. Rotation2. Rotation

3. Translation3. Translation4. Dilation4. Dilation

Called rigidWhy?

The number of position in which the object looks exactly the same is called the order of symmetry

Why is the sign on the right an Order 1 ?

He dropped his pencil in the water

How can it reflect on the Coordinate plane?

• Over:1) x- axis2) y- axis3) Vertical line, ex. x = 44) Horizontal line, ex. y = -25) Diagonal line y = x or y = -x

* The line is your mirror

Transfromations

1. Reflection y

x

Reflect the triangle usingthe line:

x = 1

* Two different mirrors, reflect over x=1 first, then that reflection over x = 5

Reflect over y=x* Special mirror *

y

x

y

x

Reflect the Triangleover the line y = -1

Reflect the triangle over The line y = -x

* Special mirror *