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Matrix Transformations for Polygons

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  1. Lesson 8.7 Transformations with Matrices To review matrix addition and multiplication To use matrices to represent transformations of polygons To solve problems using matrix models

  2. You can use a matrix to represent the vertices of a polygon graphed on a coordinate axis. • Each column contains the x- and y-coordinate of a vertex. The first row contains all the x-coordinates and the second row contains all the y-coordinates. • Vertices are in consecutive order.

  3. Matrix Multiplication • Create a set of coordinate axes on graph paper. Draw the triangle that is represented by this matrix • Add

  4. Draw the image represented by your answer to the last matrix addition. Describe the transformation. • How is the transformation related to the matrix that you added?

  5. Repeat the last procedure with each of these transformation. Use a new set of coordinate axes for each transformation.

  6. Write matrix equations to represent these translations.

  7. Draw this quadrilateral on your own graph paper. Write the coordinates of the vertices in a matrix, [B]. • Add a fifth column to your matrix to represent any point of the form (x,y). Multiply

  8. Draw the image represented by your answer the last question. • Describe the resulting transformation. • How is the last column of the image matrix related to the transformation you made using lists in this chapter? • Repeat the previous slide with • Make a conjecture about the relationship between the matrix multiplication by [B] and the resulting transformation.

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