Translating Pictures
Task
Create an interactive activity that allows you to translate a picture by a given vector and explore the characteristics of a translation.
Instructions
| 1. | Make sure that you have the picture of Bart Simpson saved on your computer before you start the actual construction. | |
| 2. | 
| Create a point A at the coordinates A = (1, 1) using the Point tool. |
| 3. | 
| Select the Image tool and click on point A in order to insert the picture of Bart at this position. |
| Hint: GeoGebra will automatically create the second corner point B of the picture. | ||
| 4. | 
| Create point D = (1, 3.9).
Hint: you might want to enter the coordinates directly into the Algebra Input. |
| 5. |  | Set point D as the FOURTH corner point of the picture (Properties dialog, tab Position). |
| 6. |  | Create a rigid triangle ABD using tool Rigid Polygon. Hint: The resulting polygon will keep its shape when moved. It can be moved or rotated by dragging two vertices. |
Try it yourself...
Instructions (continued)
| 7. |
| Create points O = (0, 0) and P = (3, -2). |
| 8. |  | Create vector u = Vector[O, P].
Hint: You may either use tool Vector or enter the command directly in the Algebra Input. |
| 9. |  | Translate the picture by vector u using tool Translate by Vector. Hint: You might want to reduce the opacity of the image (Properties dialog, tab Color). |
| 10. | | Translate the triangle ABD by vector u. Hint: This will also translate the three corner points A, B, and D by vector u. |
| 11. |  | Hide point O so it can’t be moved accidentally by using the Show / Hide Object tool. |
| 12. |  | Change the color and size of objects to enhance your construction using the Style Bar. |
Back to school...
Move the translation vector by dragging point P.
- Try to find at least one vector that moves the translated image into the second quadrant of the coordinate system and write it down.
- Also, find vectors that move the translated image into the third and fourth quadrant.
- Find the vector that moves the translated image of Bart exactly on top of the original picture and write it down.