Translations Using Matrices

In this activity, you examine how matrices can be used to represent cartoon figures and their translations.

1. The figure below is an image of a cartoon face named Skip. Label the coordinates of skips cap:

2. Matrix C below represents Skip’s cap. Matrix C’ represents his cap after a translation. Graph the new position of skips cap defined by these matrices.

3. Determine the changes that have occurred in the coordinates of each point of Skip’s cap. Write this as a vertex.

4. A matrix equation in the following form, where T is a translation matrix can be used to represent the change in position of Skip’s cap:

C + T = C’

Determine a matrix T that makes this equation true.

5. Use your calculator to check if your answer above is correct.

6. What translation matrix would you use to move Skip’s cap by the translation vector <-4,-5>?

7. Describe how you would determine the dimensions of a matrix necessary to translate any given figure by matrix addition.

8. A quadrilateral has vertices at (1, 1), (5,1), (4,4) and (0,4). Determine its image under the translation vector <4, -2> by completing parts a and b.

a) Write a matrix equation for the translation using matrix addition

b) Draw a coordinate plane below and create a graph of this translation.