14.7d The Inverse of a Translations
What is the inverse of a translation, or composition of translations?
1. Click on the checkbox to begin, and create a translation for triangle ABC by dragging the brown vector. Note that a or b or both can be negative.
2. Click on the second checkbox and drag the red vector to create the translation that maps triangle A'B'C' back to its pre-image, ABC. What are the values for c and d?
3. Reset the vectors to their original positions, (0, 1), and click on the third checkbox.
4. Drag the brown vector to create translation T. Drag the red vector for T-squared. Note that T-squared means the translation T applied twice, first to the pre-image ABC, and then to the image of ABC under T. What are the values for c and d?
5. Drag the orange vector to map the second image back to the pre-image ABC. What are the values of f and g?