Transformations
Time: Four class periods each 40 minutes
Target audience: Math 8
Required Previous Knowledge: How to plot points on a coordinate graph.
Required Materials: Rulers, graph paper, pencils
This project is designed to conclude the geometric transformations unit with students. It
includes a review of translations, reflections, rotations and dilations on the coordinate grid.
Students will find the rules for what happens to coordinates under various transformations.
Students will be separated into pairs to work on the project. Each student has a unique
product to make, but they can help each other as needed.
Assessment: Students will receive a grade on the graphs that they make and the conclusions
that they draw about the rules for each geometric transformation.
Student Name___________________________________________________
Date__________________________________________________________
Period_________________________________________________________
This project will be DUE on MONDAY, JANUARY 9, 2012.
There will be a late penalty of 10 points per day for turning in the project after January 9th.
No projects will be accepted after Friday, January 13.
1
Transformations
(Then Creating Your Own Emblem.)
You are going to use your name, a coordinate graph, and some transformations to find your unique
emblem.
 First, in the name chart, write the first 6 letters of your first name. If your name is less than
6 letters long start over on your name. (See the example where Rob only has three letters and
has to start over again with the name.)
 Now write in the first 6 letters of your last name. Again if you need more letters start over at
the beginning of your name.
 Use the letter-to-number conversion chart to get the coordinates for your original shape. The
X coordinate comes from the first name and the Y coordinate comes from the last name. If any
ordered pairs duplicate, switch the x- and y-coordinates so that all coordinate pairs are unique.
 Graph your original shape on the coordinate grid on the next page by connecting the points along
the perimeter of the shape. Make sure your points are connected to form a closed figure. (This
may mean that points may not be connected in order.)
 Pat yourself on the back … you're doing great.
Letter
AB
CD
EF
GH
IJ
KL
MN
OP
QR
ST
UV
WX
YZ
Value
1
2
3
4
5
6
7
8
9
10
11
12
13
Example:
First
R
O
B
R
O
B
Last
S
M
I
T
H
S
X
9
8
1
9
8
1
Y
10
7
5
10
4
10
Coordinate
(9,10)
(8,7)
(1,5)
(1,10)
(8,4)
(9,10)
Original Figure
First
Last
X
A
A’
B
B’
C
C’
D
D’
E
E’
F
F’
2
Y
Coordinate
Transformations
Graph your Original Figure


Using the coordinates from the previous page, graph your original figure. Be sure to rewrite your coordinates
in the table provided.
Make sure ALL shapes you graph form closed figures.
Translation (x – 5, y – 8)
A translation is taking the original image and sliding it without turning it.





Graph your original shape again.
Now translate the shape by sliding the origin 5 spaces left and 8 spaces down.
Find the coordinates for the image. (The new resulting shape)
Graph the image on the coordinate graph.
In at least one complete sentence, describe what happened to the coordinates after the transformation.
Translation (x + 2, y + 0)
A translation is taking the original image and sliding it without turning it.





Graph your original shape again.
Now translate the shape by sliding the origin 2 spaces right and 0 spaces up or down.
Find the coordinates for the image. (The new resulting shape)
Graph the image on the coordinate graph.
In at least one complete sentence, describe what happened to the coordinates after the transformation.
Reflection in the X–Axis
A reflection is taking the original image and flipping it along a line of reflection.





Graph your original shape again.
Now reflect the shape in the x-axis
Find the coordinates for the image. (The new resulting shape)
Graph the image on the coordinate graph.
In at least one complete sentence, describe what happened to the coordinates after the transformation.
Reflection in the Y–Axis
A reflection is taking the original image and flipping it along a line of reflection.





Graph your original shape again.
Now reflect the shape in the y-axis.
Find the coordinates for the image. (The new resulting shape)
Graph the image on the coordinate graph.
In at least one complete sentence, describe what happened to the coordinates after the transformation.
3
90 Clockwise Rotation
A rotation is one kind of transformation. In a rotation, the shape is turned around some point. You will rotate
your shape around the point called the origin, (0, 0).





Graph your original shape again.
Rotate the figure 90 degrees clockwise.
Find the coordinates for the image. (The new resulting shape)
Graph the image on the coordinate graph.
In at least one complete sentence, describe what happened to the coordinates after the transformation.
180 Rotation
A rotation is one kind of transformation. In a rotation, the shape is turned around some point. You will rotate your
shape around the point called the origin, (0, 0).





Graph your original shape again.
Rotate the figure 180 degrees.
Find the coordinates for the image. (The new resulting shape)
Graph the image on the coordinate graph.
In at least one complete sentence, describe what happened to the coordinates after the transformation.
90 Counter-Clockwise Rotation
A rotation is one kind of transformation. In a rotation, the shape is turned around some point. You will rotate
your shape around the point called the origin, (0, 0).





Graph your original shape again.
Rotate the figure 90 degrees counter-clockwise.
Find the coordinates for the image. (The new resulting shape)
Graph the image on the coordinate graph.
In at least one complete sentence, describe what happened to the coordinates after the transformation.
Dilation of Scale Factor 0.5
A dilation is one kind of transformation. In a dilation, the shape’s size is either enlarged or reduced. You will
dilate your shape using a scale factor of 0.5.





Graph your original shape again.
Dilate the figure using a scale factor of 0.5.
Find the coordinates for the image. (The new resulting shape)
Graph the image on the coordinate graph.
In at least one complete sentence, describe what happened to the coordinates after the transformation.
Your Emblem
Now to make your emblem, which will stand for you:
 Graph your original image
 Carry out 2 or more transformations on the same graph
 Color or decorate.
 Think of a slogan or motto to go with your emblem and write it underneath.
4
Original Figure
y
x
Original Figure
X
Y
A
B
C
D
E
F
5
Transformation #1: Translation (x – 5, y – 8)
y
x
Image
Translation (x–5, y–8)
X
Y
Original Figure
X
Y
A
B
C
A’
B’
C’
D
E
F
D’
E’
F’
What happened to the coordinates?
6
Transformation #2: Translation (x + 2, y + 0)
y
x
Image
Translation (x+2, y+0)
X
Y
Original Figure
X
Y
A
B
C
D
E
F
A’
B’
C’
D’
E’
F’
What happened to the coordinates?
7
Transformation #3: Reflection in the X-Axis (Rx-axis)
y
x
Image
Reflection over x–axis
X
Y
Original Figure
X
Y
A
B
C
D
E
F
A’
B’
C’
D’
E’
F’
What happened to the coordinates?
8
Transformation #4: Reflection in the Y-Axis (Ry-axis)
y
x
Image
Reflection over y–axis
X
Y
Original Figure
X
Y
A
B
C
D
E
F
A’
B’
C’
D’
E’
F’
What happened to the coordinates?
9
Transformation #5: 90o Clockwise Rotation (R90o CW)
y
x
Image
90 Clockwise Rotation
X
Y
Original Figure
X
Y
A
B
A’
B’
C
D
E
F
C’
D’
E’
F’
What happened to the coordinates?
10
Transformation #6: 180o Rotation (R180o)
y
x
Image
180 Clockwise Rotation
X
Y
Original Figure
X
Y
A
A’
B
C
D
E
F
B’
C’
D’
E’
F’
What happened to the coordinates?
11
Transformation #7: 90o Counter-Clockwise Rotation (R90o CCW)
y
x
A
Image
90 Counter-Clockwise Rotation
X
Y
A’
B
C
D
E
F
B’
C’
D’
E’
F’
Original Figure
X
Y
What happened to the coordinates?
12
Transformation #8: Dilation of Scale Factor 0.5 (D0.5)
y
x
Image
Dilation with Scale Factor 0.5
X
Y
Original Figure
X
Y
A
B
C
D
E
F
A’
B’
C’
D’
E’
F’
What happened to the coordinates?
13
Your Emblem
y
x
Your Motto:
14