1.2: Transformations CCSS 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. 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.

Original shape or object. Shape or object after it has been moved. Pre image Original shape or object. Image Shape or object after it has been moved. (read as A prime)

Transformation Definition – anything that maps (or moves) a pre image to an image. 4 Basic types of transformations: 1. Reflection 2. Rotation 3. Translation 4. Dilation Called rigid Why?

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- axis 2) y- axis 3) Vertical line, ex. x = 4 4) Horizontal line, ex. y = -2 5) Diagonal line y = x or y = -x * The line is your mirror

y x x = 1 Transfromations 1. Reflection Reflect the triangle using the 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 Triangle over the line y = -1

Reflect the triangle over The line y = -x * Special mirror *