Transformations

MathScience Innovation Center

Betsey Davis

Transformations B. Davis 2005 MathScience Innovation Center

Transformation= change Isometry

Translation

Reflection

– Over a line

– Around a point

– Lines of Symmetry

Dilation

Copy these down and skip lines to

keep notes.Notes graded

today !

Transformations B. Davis 2005 MathScience Innovation Center

Isometry

Change that preserves lengths and angle measures

Example:

isometric

Example:

Not isometric

Transformations B. Davis 2005 MathScience Innovation Center

Isometry

Isometry or not?

NOT !

Translations

By: Alisa

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Use the tip of the cow’s ear as the starting point (0,4)

By: Alisa

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Original f(x)

Translated up

New equation: f(x)+4

By: Alisa

Transformations B. Davis 2005 MathScience Innovation Center

Translation = slip or slide

Up Down Right Left

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Original f(x)

Translated down

New equation: f(x)-6

By: Alisa

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Original f(x)Translated left

New equation:

f(x+7)

By: Alisa

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Original f(x)

Translated right

New equation: f(x-8)

By: Alisa

Transformations B. Davis 2005 MathScience Innovation Center

Transformations B. Davis 2005 MathScience Innovation Center

2

-2

-5 5

By Camille

Transformations B. Davis 2005 MathScience Innovation Center

2

-2

-5 5

By Camille

Transformations B. Davis 2005 MathScience Innovation Center

Reflection over a line: Flip

Up and down Left and right

Transformations B. Davis 2005 MathScience Innovation Center

2

-2

-5 5

By Camille

Transformations B. Davis 2005 MathScience Innovation Center

2

-2

-5 5

By Camille

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation Rather than flip over a line-

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation Rather than flip over a line-

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation Rather than flip

over a line-

Line Reflection The line is called the line of symmetry

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation Rather than flip

over a line-

Line Reflection

Spin about a point

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation Rather than flip

over a line-

Line Reflection

Spin about a point

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation Rather than flip

over a line-

Line Reflection

Spin about a point

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation 30 degrees 90 degrees 180 degrees ¾ of a turn

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation 30 degrees 90 degrees 180 degrees ¾ of a turn

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation 30 degrees 90 degrees 180 degrees ¾ of a turn

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation 30 degrees 90 degrees 180 degrees ¾ of a turn

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation 30 degrees 90 degrees 180 degrees ¾ of a turn

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation 30 degrees 90 degrees 180 degrees ¾ of a turn

Transformations B. Davis 2005 MathScience Innovation Center

Refection:

Over line About a point

Transformations B. Davis 2005 MathScience Innovation Center

Refection:

Over line About a point

Transformations B. Davis 2005 MathScience Innovation Center

Refection:

Over line About a point

Transformations B. Davis 2005 MathScience Innovation Center

Refection:

Over line About a point

Transformations B. Davis 2005 MathScience Innovation Center

Refection:

Over line About a point

Transformations B. Davis 2005 MathScience Innovation Center

Refection:

Over line About a point

Transformations B. Davis 2005 MathScience Innovation Center

Refection:

Over line About a point

Transformations B. Davis 2005 MathScience Innovation Center

Lines of Symmetry

To count lines of symmetry, imagine how many times you can rotate image and match original

Example: a square has 4 lines of symmetry but a rectangle only has 2

Transformations B. Davis 2005 MathScience Innovation Center

Lines of Symmetry

To count lines of symmetry, imagine how many times you can rotate image and match original

Example: How many lines does a regular pentagon have?

Example: How many lines does a non-regular pentagon have?

By: Stephanie Hill

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie Hill

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie Hill

Transformations B. Davis 2005 MathScience Innovation Center

Dilation: Stretch or Shrink

Vertically: taller or shorter Horizontally: fatter or skinnier

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie Hill

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie

Transformations B. Davis 2005 MathScience Innovation Center

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

By: Stephanie

Transformations B. Davis 2005 MathScience Innovation Center

Transformation= change

Hopefully you have notes now on all of this.We add one more item

now.Notes graded today !

Isometry

Translation

Reflection

– Over a line

– Around a point

– Lines of Symmetry

Dilation

Transformations B. Davis 2005 MathScience Innovation Center

Tessellation

Completely covering a plane with

shapes with

– No overlapping

– No gaps

Here is one more.

Notes graded today !

Transformations B. Davis 2005 MathScience Innovation Center

Tessellation

A

B

D

C

MO

RT

U

V

WY

B1

C1

D1

E1

F1

G1I1

V1

W1

X1

Y1

Z1

A2

B2

C2

D2

E2

F2

G2

H2

J2

K2L2

M2

N2

O2

P2

Q2

S2T2

U2

W2

X2

Y2

Z2

B3

C3

D3

E3

F3

G3

H3

I3

V3X3

Y3

Z3

A4

B4

C4

F4H4

S4

T4

U4W4

X4

Y4

B5

I5

J5

K5

L5

M5

N5

O5

P5

Q5

R5

S5

T5

W5Y5

B6D6

E6

F6

G6

H6

I6

J6

K6

L6

M6

N6

O6

P6

Q6

R6

S6

T6

U6

V6

W6

X6

Y6

Z6

A7C7 D7

E7

F7

G7

H7

I7

K7

L7

M7

N7

O7P7

Q7

R7

S7

D8

U9

Z9A10

B10

C10

D10

E10

F10

G10

H10

L10

P10

I11

M11O11

P11

Q11

R11

S11

T11

W11Y11 Z11

A12

B12

C12

D12

E12

F12

G12

Transformations B. Davis 2005 MathScience Innovation Center

A

B

C

D

E

F

G

H

I

J

K

L

N

O

P

Q

R

S

U

W

X

Y

Z

A1

B1

C1

D1

E1

F1G1

H1

I1

J1

K1

M1

N1

O1

P1

Q1

R1

S1

T1

U1

V1

Y1

C2

F2

H2

I2

J2

L2

D3

T3

W4

Y4

A5

B5

C5

D5

E5

F5

H5

L5

P5

Q5

R5

S5

T5

U5

V5

W5

X5

Y5

Z5

A6

B6

C6

D6E6

G6

H6

I6

J6

K6

L6

M6

N6

O6

P6

Q6

R6

S6

T6

U6

V6

W6

X6

Y6

Z6

A7

B7

C7

D7

E7

F7

G7

H7

I7

J7

Transformations B. Davis 2005 MathScience Innovation Center

http://www.learnalberta.ca/Math/math6web/math6shell.swf

This website reviews translations and line reflections.

http://michaelshepperd.tripod.com/resources/tessellations.html

This website shows tessellations.

Transformations B. Davis 2005 MathScience Innovation Center

Geometry in Art

Time to practice!

translation

translation

Rotation

Or reflection about a point

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Choose the best answer

A. translation

B. line reflection

C. point reflection

or rotation

D.Dilation

E. tessellation

Transformations B. Davis 2005 MathScience Innovation Center

Sample Classwork

Chesterfield County Public Schools Geometry: Page 399 # 5,6,7 # 21 ,22 (just name transformation) 23,24,25,42 Page 407 #3,4,5,12,13,14