Name____________________________
Date_____________________
Transformation Project – Isometric Transformations
This is a 100 point project (test grade). This is due Friday December 13th, 2013
You will be practicing the transformations that we learned about in class including:
1. Translation
2. Reflection
3. Rotation
You will choose one object that does NOT have rotational symmetry. This object must have at least 6
ordered pairs. You may use your initials, a sketch, or you may trace an object.
For each task, you must identify the original coordinates (you can select 6 of them) and the new
coordinates after the isometric transformation and show the original and final transformation on a
graph (several graphs are included for your use and it may be easiest to use these in landscape mode).
Each set of transformations below must be on a separate piece of graph paper and labelled correctly.
Grading:
A) Each Transformation - 20 points for each of 8 transformations (160 total)
a. Correct transformation(s) on the graph including labels (object names must be
included) – 10 points
b. Correct coordinates – 5 points (no credit if A is incorrect)
c. Answers to questions – 5 points
B) Creativity – 10 points (10 total)
C) Effort – based on neatness – 10 points (10 total)
D) Conclusions about isometric transformations – 20 points (20 total)
Perfect score is 200 points.
1. Transformation 1: Your original object starts in quadrant 1. Label this object 1. Translate object 1
into quadrant 3. Label this object 2. Describe the translation algebraically and show how this was
used to get to the final destination.
Algebraic Translation (
,
)
Original Coordinates:
Final Coordinates:
What is the relationship between an original object and its coordinates when it is translated? (Does it
look the same except it is in different place – if so, how did it get there? or is the object flipped or
turned?)
1
2. Transformation 2: Your original object starts in quadrant 3. Label this object 1. Reflect your object
across the x-axis labeling this object 2. Reflect object 2 across the y-axis and label this object 3.
Reflect object 1 across the y-axis and label this object 4.
Original Coordinates:
Final Coordinates object 2:
Final Coordinates object 3:
Original Coordinates:
Final Coordinates object 4:
What is the relationship between an original object and its coordinates when it is reflected across the xaxis?
What is the relationship between an original object and its coordinates when it is reflected across the yaxis?
3. Transformation 3: Your original object starts in quadrant 2. Label this object 1. Rotate object 1 90°
clockwise. Label this object 2.
Original Coordinates:
Final Coordinates object 2:
What is the relationship between an original object and its coordinates when it is rotated 90° clockwise?
2
4. Transformation 4: Your original object starts in quadrant 2. Label this object 1. Rotate object 1 90°
counter-clockwise. Label this object 3.
Original Coordinates:
Final Coordinates object 3:
What is the relationship between an original object and its coordinates when it is rotated 90° counterclockwise?
5. Transformation 5: Your original object starts in quadrant 2. Label this object 1. Rotate object 1
270° counter-clockwise. Label this object 4.
Original Coordinates:
Final Coordinates object 4:
What is the relationship between an original object and its coordinates when it is rotated 270° counterclockwise?
What is the relationship between object 2 from transformation 3 and object 4 from this
transformation?
6. Transformation 6: Your original object starts in quadrant 2. Label this object 1. Rotate object 1
180° counter-clockwise. Label this object 5.
Original Coordinates:
Final Coordinates object 5:
What is the relationship between an original object and its coordinates when it is rotated 180° counterclockwise?
3
7. Transformation 7: Your original object starts in quadrant 2. Label this object 1. Rotate object 1
180° clockwise. Label this object 6.
Original Coordinates:
Final Coordinates object 6:
What is the relationship between an original object and its coordinates when it is rotated 180°
clockwise?
What is the relationship between object 5 (prior transformation) and object 6?
8. Transformation 8: create your own transformation which combines a translation, rotation, and
reflection. Describe it below and label your transformations on the graph.
Original Coordinates:
Final Coordinates:
4
Describe your transformations below.
Identify the patterns - Look over your work from the project and pick a single point. Note that the
answer to the question below the tables should be written in terms of x and y.
Transformation 2:
a. Reflection across the x-axis – Transformation 2 Original Point (Pre-image) object 1
Transformed Point (Image) object 2
When reflecting over the x-axis, the _____-coordinate becomes __________________.
b. Reflection across the y-axis – Transformation 2
Original Point (Pre-image) object 1
Transformed Point (Image) object 4
When reflecting over the y-axis, the _____-coordinate becomes __________________.
c. Reflection across the x & y axis – Transformation 2
Original Point (Pre-image) object 1
Transformed Point (Image) object 3
When reflecting over the x-axis, and then the y-axis, the x-coordinate and y-coordinate become
__________________.
5
Transformation 3:
a. Rotation 90° clockwise Transformation 3 Original Point (Pre-image) object 1
Transformed Point (Image) object 2
When rotating an object 90° clockwise , the (x,y) coordinates changes as follows (include as changes in
signs) __________________.
Transformation 4:
a. Rotation 90° counter-clockwise Transformation 3 Original Point (Pre-image) object 1
Transformed Point (Image) object 3
When rotating an object 90° counter-clockwise , the (x,y) coordinates changes as follows (include as
changes in signs) __________________.
Transformation 5:
a. Rotation 270° counter-clockwise Transformation 3 Original Point (Pre-image) object 1
Transformed Point (Image) object 4
When rotating an object 270° counter-clockwise , the (x,y) coordinates changes as follows (include as
changes in signs) __________________.
Compare this to Transformation 3 – what did you find?
Transformation 6:
a. Rotation 180° counter-clockwise Transformation 3 Original Point (Pre-image) object 1
Transformed Point (Image) object 5
When rotating an object 180° counter-clockwise , the (x,y) coordinates changes as follows (include the
changes in signs) __________________.
Compare this to Transformation 2 – object 3 – what did you find?
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Transformation ___
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