Transformations
MathScience Innovation Center
Betsey Davis
Transformation= change

Isometry

Translation

Reflection
– Over a line
– Around a point
– Lines of Symmetry

Dilation
Transformations B. Davis
2005
MathScience Innovation Center
Copy these down
and skip lines to
keep notes.
Notes graded
today !
Isometry

Change that preserves lengths and
angle measures
Example:
Example:
isometric
Not isometric
Transformations B. Davis
2005
MathScience Innovation Center
Isometry

Isometry or not?
NOT !
Transformations B. Davis
2005
MathScience Innovation Center
Translations
By: Alisa
8
6
Use the tip of the
cow’s ear as the
starting point (0,4)
-10
4
2
-5
5
-2
-4
-6
By: Alisa
Transformations B. Davis
2005
-8
MathScience Innovation Center
10
8
Translated up
New equation:
f(x)+4
6
4
2
-10
-5
5
10
-2
-4
Original f(x)
-6
By: Alisa
Transformations B. Davis
2005
-8
MathScience Innovation Center
Translation = slip or slide
Up
 Down
 Right
 Left

Transformations B. Davis
2005
MathScience Innovation Center
8
6
Original f(x)
4
2
-10
-5
5
Translated down
-2
New equation: f(x)-6
-4
-6
Transformations B. Davis
By:
Alisa
-8
2005
MathScience Innovation Center
10
8
6
4
2
-10
-5
5
10
Original f(x)
Translated left
-2
-4
New equation:
-6
f(x+7)
Transformations B. Davis
By:
Alisa
-8
2005
MathScience Innovation Center
8
Translated
right
6
4
2
-10
-5
5
-2
Original f(x)
-4
-6
Transformations B. Davis
By:
Alisa
-8
2005
MathScience Innovation Center
10
New
equation:
f(x-8)
Transformations B. Davis
2005
MathScience Innovation Center
By Camille
2
-5
5
-2
Transformations B. Davis
2005
MathScience Innovation Center
By Camille
2
-5
5
-2
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
By Camille
2
-5
5
-2
Transformations B. Davis
2005
MathScience Innovation Center
2
-5
5
-2
By CamilleTransformations 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
Transformations B. Davis
2005
The line is called the line
MathScience Innovation Center
of symmetry
Reflection about a point= rotation

Rather than flip
over a line-
Spin
Line Reflection
Transformations B. Davis
2005
MathScience Innovation Center
about a point
Reflection about a point= rotation

Rather than flip
over a line-
Spin
Line Reflection
Transformations B. Davis
2005
MathScience Innovation Center
about a point
Reflection about a point= rotation

Rather than flip
over a line-
Spin
Line Reflection
Transformations B. Davis
2005
MathScience Innovation Center
about a point
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
Transformations B. Davis

2005
About a point
MathScience Innovation Center
Refection:

Over line
Transformations B. Davis

2005
About a point
MathScience Innovation Center
Refection:

Over line
Transformations B. Davis

2005
About a point
MathScience Innovation Center
Refection:

Over line
Transformations B. Davis

2005
About a point
MathScience Innovation Center
Refection:

Over line
Transformations B. Davis

2005
About a point
MathScience Innovation Center
Refection:

Over line
Transformations B. Davis

2005
About a point
MathScience Innovation Center
Refection:

Over line
Transformations B. Davis

2005
About a point
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?
Transformations B. Davis
2005
MathScience Innovation Center
By: Stephanie Hill
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Hill
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Hill
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
Dilation: Stretch or Shrink
Vertically: taller or shorter
 Horizontally: fatter or skinnier

Transformations B. Davis
2005
MathScience Innovation Center
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Hill
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
8
6
4
2
-10
-5
5
-2
-4
-6
By:
Stephanie
Transformations
B. Davis
2005
MathScience Innovation Center
-8
10
Transformation= change

Isometry

Translation

Reflection
– Over a line
Hopefully you have
notes now on all of this.
We add one more item
now.
Notes graded today !
– 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
Transformations B. Davis
2005
MathScience Innovation Center
Here is one
more.
Notes graded
today !
Tessellation
M
B10
CS
552
W2
S
T
H72662
V
X
K
YU42
P
LK27272
F
H
T
D
5
10
H
B
Q
32 5
IJK
O
L910
Q
Z
AN
66
52
7
N521
FO
R
BW
12
5
10
W6
T76
G
T
R
W
IU
A
44765
AL
3U
C
7
D
M76
X4Z2
A
F
C
V11
R
4I4
5
T
Q
E
P
S
1
G
5311
676
12
J
E2
DR
G
D37J
35
D
G
B
IM
B
K12
D
6Y
P
561161
10
N
A
27
NXG
E
5110
12
V44
S
B
S
RY
11
66
X
D
U
S
FM
T
EH
3O
Z744622
Y2
Transformations B. Davis
2005
MathScience Innovation Center
Y
C31
H
P
O
C12
66
11
G2
V
X
O
P
B
Z
W
Y
Z
Y
33
H
Q
3
3510
W
P
17
511
Y
611
11
F61
Z
IE
11
11
O5
XV51
M1
R5
US51
P1
S5
B
R61
Q
J75
I1
V
T
A
UT
561
P5
Y
O
Q
P51
U751
W
G
N
D71
B
DI 3
C
F76
ZH
E751
A
D
HE676
JK1
A
G
CF
W
C
N
676
161
I7
HW
N
XJ
61
B6 6
VH
KC61
O
Z4
W
DI67
G
B
YR
661
EGY
764
LS
D
F6H
J
ZL
66L1
52
YC
OA
K
61 2
ME
B615
X
EI25
TF
32
SC65
PR
LH
65 2
TA
65
Transformations B. Davis
GK52
UY1
2005QQ
MathScience Innovation Center
DJ
F
6552
T
E22
I5G
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!
Rotation
Or reflection
about a point
translation
translation
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

Transformations B. Davis
2005
MathScience Innovation Center