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GeoGebraGeoGebra Classroom

Translations Discovery Activity

Use the tools to: 1) Create a polygon in the coordinate plane. Do this by clicking on the polygon tool (triangle with 3 blue vertices). Click on the graph to make the first vertex, click any where else on the graph to make other vertices, then click back on the first vertex to close/complete the shape. It does not matter what the shape is. Click on all the vertices (use ctrl to select more than one at a time) then click on the lock to lock the shape in place. 2) Label the vertices. Right click on the point(s), go to settings, make sure "show label" is checked and change it to show name AND label. You should now be able to see the letter and coordinate of each of your vertices. 3) Use the vector tool to create a vector with the endpoint at the origin. You can choose to make the vector point in any direction you choose with any magnitude (length). Label the vector with the name and label. You should be able to see what looks like an order pair for the vector. This tells you the direction and magnitude of that particular vector.

Translate your shape.

Now, use the "translate by vector tool" to translate your figure. Click on the translate by vector tool, click on your vector, then click on your shape. You should now see an image and pre-image. You can make the vector shorter, longer, or change direction - your image should move each time you do that. How does a vector help translate a shape? What do you notice about your pre-image and image and the vector?

Making connections

Use the vector to write the mapping notation and subscript notation for your translation.