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Ch.8.7_Reflections.notebook                                                           March 05, 2012


                                 Chapter 8.7
                                 Reflections Using Matrices



                                                           What are the coordinates
                                                           of the vertices?




                                  Express the vertices as a matrix




                         We can perform reflections using special
                         2x2 matrices and vertex matrices


                       Reflection Matrices
                                                                over y = x
                       over x­axis
                                                                     0  1
                        1   0
                                                                     1  0
                        0  ­1

                                                                 over y = ­x
                        over y­axis
                                                                      0  ­1
                         ­1  0                                       ­1  0
                          0  1




                                      Reflect the image above
                                      over the line y = ­x
                         0  ­1
                        ­1  0




                                                                                                       1
Ch.8.7_Reflections.notebook                               March 05, 2012

                              Perform all 4 reflections




                                                                           2
Ch.8.7_Reflections.notebook      March 05, 2012




                      Page 370
                      1 ­ 14




                                                  3

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Ch.8.7 Reflections

  • 1. Ch.8.7_Reflections.notebook March 05, 2012 Chapter 8.7 Reflections Using Matrices What are the coordinates of the vertices? Express the vertices as a matrix We can perform reflections using special 2x2 matrices and vertex matrices Reflection Matrices over y = x over x­axis 0  1 1   0 1  0 0  ­1 over y = ­x over y­axis  0  ­1 ­1  0 ­1  0  0  1 Reflect the image above over the line y = ­x  0  ­1 ­1  0 1
  • 2. Ch.8.7_Reflections.notebook March 05, 2012 Perform all 4 reflections 2
  • 3. Ch.8.7_Reflections.notebook March 05, 2012 Page 370 1 ­ 14 3