Intro to Transformations
Geometry
Name_________________________ Block___
Objective: Identify and describe the rigid transformations: translations, reflections, and rotations.
EQ: How would transformations be used outside of Geometry and mathematics?
This activity will give you an introduction to three types of
transformations: translations, reflections, and rotations. These
types of transformations are called rigid transformations because
they preserve the distance between every pair of points. In other
words, the size of the image will not change, only its position and
orientation.
Instructions to begin:
1) Open ‘Internet Explorer’
2) Enter the URL http://goo.gl/TUSR7z and press ‘Enter’
Capital Letters Matter! ( T U S R 7 z )
3) Below ‘Transformations Interactive.xlsx’ click ‘File’ and
‘Download’
4) At the bottom of the screen, click ‘Open’
5) After the file opens in Microsoft Excel, click ‘Enable Editing’
at the top of the screen
Your screen should now look like this:
6) Complete the introduction steps on
the computer to begin Part 1 of this
worksheet.
Intro to Transformations
Geometry
Part 1 – Translations
1) Write the definition of Translation:
2) Enter these X and Y points into the document.
These points produce an image called the Pre-Image: the original figure prior to transformation
Pre-Image
Point
A
B
C
D
X
Y
3
0
-3
-2
2
4
5
3
-1
-3
Coord.
(3,4)
(0,5)
(-3,3)
(-2,-1)
E
(2,-3)
3) Enter a number between -5 and 5 underneath ‘X Translation’. What was this number?
How did the Red graph change?
4) Try a different number. What was this number?
How did the Red graph change this time?
5) Change the number under ‘X Translation’ to zero (0).
6) Enter a number between -5 and 5 underneath ‘Y Translation’. What was this number?
How did the Red graph change?
7) Try a different number. What was this number?
How did the Red graph change this time?
8) Enter a new number between -5 and 5 underneath both ‘X and Y Translation’, copy these below.
Translation
X Translation
Y Translation
The Red graph produced is the Image: the result of a transformation
9) Find the points of the image that correspond to points of the pre-image. Copy these below once you
have them all correct on the screen.
Image
Point'
A'
B'
C'
D'
X
Y
Coord.
( , )
( , )
( , )
( , )
E'
( , )
10) Compare the difference between the X points of the pre-image with the X points of the image. How far
apart are they? Is this the same number as the ‘X Translation’?
11) Repeat question 10 with the Y points. How far apart are they? Is it the same as your ‘Y Translation’?
Intro to Transformations
Geometry
Part 1 – Translations Continued
12) Sketch and label your Pre-Image and your Image on the graph space below.
13) Write a summary about translations. How does a translation affect the pre-image to produce the
image? Use what you have discovered as an example.
Now write your response into the Google Document
You may now click the link that says ‘Continue to part 2’, or click the ‘Reflections’ tab at the bottom.
Intro to Transformations
Geometry
Part 2 – Reflections
1) Write the definition of Reflection:
2) Enter these X and Y points into the document.
Pre-Image
Point
A
B
C
D
X
Y
-1
2
7
8
3
2
7
9
4
-1
X
Y
Coord.
(-1,2)
(2,7)
(7,9)
(8,4)
E
(3,-1)
3) Change the ‘Reflection Type’ to ‘X-Axis’ and find the points of the Image
Image
Point'
A'
B'
C'
D'
Coord.
( , )
( , )
( , )
( , )
E'
( , )
4) Compare the X and Y values of the Image and Pre-Image. Are they the same? Different?
5) Change the ‘Reflection Type’ to ‘Y-Axis’ and find the points of the Image
Image
Point'
A'
B'
X
Y
C'
D'
Coord.
( , )
( , )
( , )
( , )
E'
( , )
6) Compare the X and Y values of the Image and Pre-Image. Are they the same? Different?
7) Change the ‘Reflection Type’ to ‘X- and Y-Axis’ and find the points of the Image
Image
Point'
A'
B'
C'
D'
X
Y
Coord.
( , )
( , )
( , )
( , )
E'
( , )
8) Compare the X and Y values of the Image and Pre-Image. Are they the same? Different?
Intro to Transformations
Geometry
Part 2 – Reflections Continued
9) Sketch and label your Pre-Image and your Image from the final reflection over the X- and Y-Axis on the
graph below.
10) Write a summary about reflections. How does a reflection affect the points of the pre-image to produce
the image? Use what you have discovered as an example.
Now write your response into the Google Document
You may now click the link that says ‘Continue to part 3’, or click the ‘Rotation’ tab at the bottom.
Intro to Transformations
Geometry
Part 3 – Rotations
1) Write the definition of Rotation:
2) Enter these X and Y points into the document.
Pre-Image
Point
A
B
C
D
X
Y
2
3
6
8
5
2
5
6
2
1
X
Y
Coord.
(2,2)
(3,5)
(6,6)
(8,2)
E
(5,1)
3) Change the ‘Rotation Type’ to ’90 Degrees Counter-Clockwise’ and find the points of the Image
Image
Point'
A'
B'
C'
D'
Coord.
( , )
( , )
( , )
( , )
E'
( , )
4) Compare the X and Y values of the Image and Pre-Image. Are they the same? Different?
5) Change the ‘Rotation Type’ to ‘180 Degrees Counter-Clockwise’ and find the points of the Image
Image
Point'
A'
B'
X
Y
C'
D'
Coord.
( , )
( , )
( , )
( , )
E'
( , )
6) Compare the X and Y values of the Image and Pre-Image. Are they the same? Different?
7) Change the ‘Rotation Type’ to ‘270 Degrees Counter-Clockwise’ and find the points of the Image
Image
Point'
A'
B'
C'
D'
X
Y
Coord.
( , )
( , )
( , )
( , )
E'
( , )
8) Compare the X and Y values of the Image and Pre-Image. Are they the same? Different?
Intro to Transformations
Geometry
Part 3 – Rotations Continued
9) Sketch and label your Pre-Image and your Image from the final rotation of 270 degrees counterclockwise on the graph below.
10) Write a summary about rotations. How does a rotation affect the points of the pre-image to produce the
image? Use what you have discovered as an example.
Now write your response into the Google Document