Slide to the Left, Slide to the Right!!!

Transformations on the Coordinate Plane

Dilations

Dilations

Rotations Rotaions

Translations

Reflections

Translations

What type of transformation does each of these graphs represent?

How can you tell?

2

31

What type of transformation does this graph represent?

How can you tell?

A B

CD

A’

B’ C’

D’

Review of Transformations

DilationDilation makes an image larger or smaller. It moves a figure on a fixed center using a scale factor. A scale factor greater than 1 enlarges; less than 1 shrinks.

TranslationTranslation slides a figure up or down, and left or right. The figure’s size and shape are unchanged.

ReflectionReflection “flips” a figure across the x-axis or y-axis. The figure’s size and shape are unchanged. We use “prime” notation when identifying new coordinates.

Rotation Rotation moves a figure around a fixed center.

Summary of Transformation FormulasHow the coordinates of each point change

with each type of transformation.

Reflection across the x- axis

Reflection across the y- axis

Translation

Dilation

Rotation 90º counterclockwise

Rotations 90˚ clockwise

Rotation 180º

(x, y) goes to (x, -y)

(x, y) goes to (-x, y)

(x, y) goes to (x + a, y + b)

(x, y) goes to (kx, ky)

(x, y) goes to (-y, x)

(x, y) goes to (y, -x)

(x, y) goes to (-x, -y)

DilationDilation makes an image larger or smaller.

The size of the figure changes. The shape of the figure stays the same.

It moves a figure on a fixed center using a scale factor. A scale factor greater than 1 enlarges; less than 1 shrinks.

Original figure:A: (-4, 8)B: (6, 8)C: (6, -6)D: (-4,-6)

Figure after dilation:A’: (-2, 4)B’: (3, 4)C’: (3, -3)D’: (-2, -3)

Dilation factork = ½

A B

CD What are the points?

What is the dilation factor?

TranslationThe figure stays the exact same size and shape.

Each point moves the same amount: to the left or right, and up or down.

Original Figure:A: (2,1)B: (6,1)C: (4,4)

Translated figure:A’: (4,-4)B’: (8,-4)C’: (6,-1)

Translation:2 units right and 5 units down

A

C

B

A’ B’

C’

What are the points?

Describe the steps in this translation.

Reflection across the y-axis

Original figure:A: (4, 2)B: (8, 2)C: (9 ,6)D: (6, 9)E: (3, 6)

Reflected figure:A’: (-4, 2)B’: (-8, 2)C’: (-9, 6)D’: (-6, 9)E’: ( -3, 6)

How have the coordinates for the points

of the original figure been changed

when the figure is reflected across the y-axis ?

What would be the coordinates if the original figure were reflected across the x-axis ?

A B

C

D

EE’

D’

C’

B’

A’

What are the points?

180˚ Rotation Around The Origin

OriginalFigure:A: (4, 2)B: (6, 2)C: (3.5, 4)D: (6.5, 4)E: (5, 5)

Figure after rotation:A’: (-4, -2)B’: (-6, -2)C’: (-3.5, -4)D’: (-6.5, -4)E’: (-5, -5)

How have the coordinates of the original figure

been changed by the 180˚ rotation around the origin?

Draw a sketch.

What are these

points?

A

B

C

P

Q

R

a) Show that D ABC is congruent to D PQR with a reflection followed by a translation.

b) If you reverse the order of the reflection and translation in part (a), does D ABC still map to D PQR ?

c) Find another way, different from part (a) or (b), to map D ABC to D PQR, using translations, rotations, and/or reflections.

Practice with transformations

Transformations Project 

For this project, you will create a poster to demonstrate your knowledge of transformations.

For each type of transformation, you will do the following on a separate graph:

•Start by graphing a figure and its transformation on a sheet of graph paper. •Use 2 different colors to distinguish the the original figure from its transformation. •Label each graph with a title telling what type of transformation it shows. •Each graph should be a different original image.•Label each vertex of the original image, then use the “prime” notation to label the corresponding vertices of the new image.•Write a paragraph explaining the transformationReflection Rotation Translation Dilation

The ParagraphWrite a paragraph about your transformations.

Describe each transformation in your own words. Include important information about each transformation

such as line of reflection, point of rotation, degrees and direction of

rotation, and specifics about the translation.

Write or print neatly and use proper grammar and spelling. Organize your transformation graphs and summary paragraph on a

poster board. (Minimum size: half of a full size poster board). Make this neat and

colorful. You will have one class period to work during school;

you may need to complete the project outside of class time. Use the rubric below to be sure you have included everything.

Score yourself on your project and record your scores in the rubric. Good luck and have fun!