What are transformations?

The word "transformation" refers to a movement or change in a

geometric shape

Introduction to Unit V- Transformations

Reflections

Definition: A reflection flips the object across a point or line. An object and its reflection have the same shape and size, but the figures face in opposite directions.

Example:

Reflections in Nature

Reflections in photography: Horizontal Reflections

Select the upper part of the image, make a copy of it, flip it over vertically and line it up to the bottom of the upper image to make a perfect reflection.

Reflections in art: Vertical Reflections

Reflections in Art

Vitruvian Man by Leonardo DivinciDivinci regularly used math in his art. In fact, he said “Let no one read me who is not a mathematician”

TranslationDefinition: A translation moves an object

without changing its size or shape and without turning it or flipping it.

So the object slides

Example: A person sliding down a water slide

Translations in Architecture

How is this an example of a translation?

Where do you see reflections in this picture?

Translations in Art

M.C. Escher

RotationsDefinition: A rotation is a transformation

that turns a figure about a fixed point called the center of rotation. 

Characteristics: An object and its rotation are the same shape and size, but the figures may be turned in different directions.

Examples of figures with rotational symmetry

Rotations in Art

Carolina Lily

Islamic ArtRosette Bearing the Name and Titles of the Emperor Shah Jahan Mir 'Ali, Calligrapher

Doors, Pair, ca. 1325–1330; Mamluk period (1250-1517)

What other transformation do you see in this picture?

Dilation

Definition: A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

Example:

Examples of Dilations

Enlarged Multinucleate Cell

Line symmetrySymmetry occurs when two halves of a figure mirror each other across a line.  The line of symmetry is the line that divides the figure into two mirror images. A simple test to determine if a figure has line symmetry is to fold the figure along the supposed line of

symmetry and see if the two halves of the figure coincide.

Horizontal Line of symmetry

A piece of artwork with two lines of symmetry

Lines of symmetry in geometric figures

Broken Star

Point Symmetry/ Rotational Symmetry

An object has rotational symmetry if there is a center point around which the object is turned (rotated) a certain number of degrees and the object looks the same. A geometric figure has rotational symmetry if the figure is the image of itself under a rotation about a point through any angle whose measure is strictly between 0º and 360º.  The angles of 0º and 360º are excluded since nothing new happens.

Example: When you are riding on a ferris wheel, you are rotating around the center of the ferris wheel