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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
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
Reflection over a line: Flip
Up and down Left and right
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
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
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