LO­9 Sequences of Transformations.notebook
Standard: G.CO5
LO­9: I can specify a sequence of transformations that will produce a desired image from a given figure.
Key Points:
• A translation is an isometry where all points in the preimage are moved parallel to a given line.
• A reflection is an isometry in which a figure is moved along a line perpendicular to a given line called the line of reflection.
• A rotation is an isometry where all points in the preimage are moved along circular arcs determined by the center of rotation and the angle of rotation.
Steps that will help in determining a sequence of transformations:
1. Draw the image of each individual transformation of a potential sequence.
2. If you are successful in mapping the given figure onto the desired image, write down the sequence in function notation. Ex: T0,6(R90°( ).
3. If you are not successful the first time, look back at the sequence you tried to determine where it went wrong.
Note: There may have been more than one transformation applied to produce a particular image.
Ex: Describe a sequence of transformations that could be used to map onto
.
y
C
B
A
x
D
A'
B'
Write the functions/rules that map ABCD to A’B’C’D’.
D'
C'
Ex: Describe a sequence of transformations that could be used to map onto
.
y
B
A
B'
C
x
Write the functions/rules that map ABC to A’B’C’.
C'
A'
LO­9 Sequences of Transformations.notebook
Worktime:
1. Specify a sequence of transformations that will map ABCD onto PQRS.
y
5
4
D
C
3
2
A
B
1
x
S
­6
­5
­4
­3
­2
P
0 1
­1
­1
P Q R S
A B C D
6
2
3
4
5
6
­2
­3
­4 Q
Write the function that maps ABCD onto PQRS.
R
­5
­6
2. Specify a sequence of transformations that will map LMNO onto WXYZ.
y
5
N
4
M
3
2
1
L
­3
­2
Z
W
O
Write the function that maps LMNO onto WXYZ.
x
­1
0
1
2
3
4
­1
5
6
7
8
X
­2
Y
­3
3. Create two different sequences using 2­3 different transformations for each. Make sure you draw the pre­image, final image, and write the functions for each sequence. Be ready to put these on the board. I want to see how creative you can be.
y
y
6
6
5
5
4
4
3
3
2
2
1
­6
­5
­4
­3
­2
­1
0
­1
1
x
1
2
3
4
5
6
­6
­5
­4
­3
­2
­1
0
­1
­2
­2
­3
­3
­4
­4
­5
­5
­6
­6
x
1
2
3
4
5
6
Sequence: Sequence: Function: Function: LO­9 Sequences of Transformations.notebook
Standard: G.CO5
LO­9: I can .
Key Points:
• A is an isometry where all points in the preimage are moved parallel to a given line.
• A is an isometry in which a figure is moved along a line perpendicular to a given line called the line of reflection.
• A is an isometry where all points in the preimage are moved along circular arcs determined by the center of rotation and the angle of rotation.
Steps that will help in determining a sequence of transformations:
1. Draw the image of each individual transformation of a potential sequence.
2. If you are successful in mapping the given figure onto the desired image, write down the sequence in function notation. Ex: T0,6(R90°( ).
3. If you are not successful the first time, look back at the sequence you tried and determine where it went wrong.
Note: There may have been more than one transformation applied to produce a particular image.
Ex: Describe a sequence of transformations that could be used to map onto
.
y
B
C
A
D
x
A'
B'
Write the functions/rules that map ABCD to A’B’C’D’.
D'
C'
Ex: Describe a sequence of transformations that could be used to map onto
.
y
B
A
B'
C
x
Write the functions/rules that map ABC to A’B’C’.
C'
A'