Name Date Transformation Project Isometric Transformations This is a 100 point project (test grade). This is due Friday December 13 th, 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 (, ) 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. Final Coordinates object 2: Final Coordinates object 3: Final Coordinates object 4: What is the relationship between an original object and its coordinates when it is reflected across the x- axis? What is the relationship between an original object and its coordinates when it is reflected across the y- axis? 3. Transformation 3: Your original object starts in quadrant 2. Label this object 1. Rotate object 1 90 clockwise. Label this object 2. 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. 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. 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. 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. 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. 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? 6
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