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9.1 Translation Vectors                                   January 20, 2012



                          9.1 Translation using Vectors

     Image: new figure
     Preimage: original figure
     Translation: slides every point the same distance




HW pg. 576 #4­28 evens                                                       1
9.1 Translation Vectors                              January 20, 2012




     Isometry: transformation that preserves length & angle 
                measure
                (congruence transformation)




HW pg. 576 #4­28 evens                                                  2
9.1 Translation Vectors                                                                    January 20, 2012

              Translation Theorem: A translation is an isometry. 
                                                B'

                               B

                                                                ABC ≅      A'B'C'
                                           A'        C'

                          A        C

               Vector: a quantity that has both direction and magnitude (size)

               Vector FG: FG                                   Terminal (ending) 
                                                               Point: G
                                                           G
                              Initial (starting)
                              Point: F                                vertical component
                                                 F

                                                     horizontal component




               Component Form: horizontal & vertical components  5,2




HW pg. 576 #4­28 evens                                                                                        3
9.1 Translation Vectors   January 20, 2012




HW pg. 576 #4­28 evens                       4
9.1 Translation Vectors   January 20, 2012




HW pg. 576 #4­28 evens                       5
9.1 Translation Vectors   January 20, 2012




       HW pg. 576 #4­28 evens




HW pg. 576 #4­28 evens                       6

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9.1 notes

  • 1. 9.1 Translation Vectors January 20, 2012 9.1 Translation using Vectors Image: new figure Preimage: original figure Translation: slides every point the same distance HW pg. 576 #4­28 evens 1
  • 2. 9.1 Translation Vectors January 20, 2012 Isometry: transformation that preserves length & angle  measure (congruence transformation) HW pg. 576 #4­28 evens 2
  • 3. 9.1 Translation Vectors January 20, 2012 Translation Theorem: A translation is an isometry.  B' B ABC ≅      A'B'C' A' C' A C Vector: a quantity that has both direction and magnitude (size) Vector FG: FG Terminal (ending)  Point: G G Initial (starting) Point: F vertical component F horizontal component Component Form: horizontal & vertical components  5,2 HW pg. 576 #4­28 evens 3
  • 4. 9.1 Translation Vectors January 20, 2012 HW pg. 576 #4­28 evens 4
  • 5. 9.1 Translation Vectors January 20, 2012 HW pg. 576 #4­28 evens 5
  • 6. 9.1 Translation Vectors January 20, 2012 HW pg. 576 #4­28 evens HW pg. 576 #4­28 evens 6