Geometry SOL G.3 Transformations Study Guide 
         Name __________________________________________________ Date_____________Block______ 
                                Transformations and Symmetry Review and Study Guide 
            Things to Know (use your notes, homework, checkpoints, as well as flashcards at 
             quizlet.com (http://quizlet.com/4695362/geometry-chapter-9-transformations-and-
             symmetry-flash-cards/).  The NY Regents Prep website 
             (http://www.regentsprep.org/regents/math/geometry/math-GEOMETRY.htm#m5) is 
             also an EXCELLENT resource.     
             o  Transformations:   
                     translation:  moves every point of a figure the same distance in the same 
                      direction; "slide"; pre-image and image are congruent (isometry) 
                           Vectors may be used to describe translations 
                     reflection:  creates a mirror image over a line of reflection; "flip"; pre-image and 
                      image are congruent (isometry) 
                           Point reflections are the same as 180 rotations 
                     rotation:  turns a figure about a fixed point called the center of rotation; "turn"; 
                      pre-image and image are congruent (isometry) 
                     dilation:  reduces or enlarges a figure to a similar figure; pre-image and image are 
                      SIMILAR, not congruent 
             o  Transformation Rules (YOU WILL NEED TO KNOW THESE!): 
                     Translations (horizontal a, vertical b):  (x, y) → (x + a, y + b)  (or vector ) 
                     Line Reflections:   
                           over x-axis:  (x, y) → (x, - y) 
                           over y-axis:  (x, y) → (- x, y) 
                           overyx:    (x, y) → ( y, x) 
                           overyx:  (x, y) → (-y, - x) 
                     Point Reflections:  (x, y) → (-x, - y) 
                     Rotations (positive rotations are counterclockwise): 
                           90:  (x, y) → (-y,  x) 
                           180:  (x, y) →  (-x, - y) 
                            270 (same as -90):  (x, y) → (y, - x) 
                     Dilations:  for scale factor k, (x, y) →  (kx, k y)   
                                          
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                                                                                                                 o  Symmetry: 
                                                                                                                                                                                                     line symmetry:  occurs when a figure can be mapped onto itself by a reflection over a 
                                                                                                                                                                                                      line of symmetry; think of folding the paper over this line and getting a match; there 
                                                                                                                                                                                                      can be no, one, or more than one line of symmetry 
                                                                                                                                                                                                     rotational symmetry:  there is a center point around which the object is turned 
                                                                                                                                                                                                      (rotated) a certain number of degrees and the object looks the same 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           o
                                                                                                                                                                                                     point symmetry:  same as rotational symmetry with degree of rotation 180 ; figure 
                                                                                                                                                                                                      looks the same upside down. 
                                                                            DO NOT LIMIT YOUR STUDYING ONLY TO PROBLEMS IN THIS STUDY GUIDE! 
                                                                            Example problems: 
                                                                            1)  Triangle A’B’C’ is the image of ABC after a translation.  Write a rule for the translation.  Write 
                                                                                                                 the rule in mapping form, (x, y)  →  (x +a, x + b), and vector component form, .  
                                                                                       a)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                b)  
                                                                             
                                                                            2)  The vertices of ABC  are A(-3, 1), B(2, 4), and C(3, 0).  Translate ABC using the given vector.  
                                                                                                                 Graph ABC and its image.  Label points.  Find vertices of transformed image. 
                                                                                       a)  <2, -3>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       b)   <-1,  -4> 
                                                                             
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
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                                                                            3)  Reflect the polygon over the given line.  Label points.  Find vertices of transformed image. 
                                                                                       a)   y-axis                                                                                                                                                                                                                                                                                                                                                                     b)   x 1                                                                                                                                                                                                                                                                                                                                                                            c)   y  x 
                                                                             
                                                                            4)  Rotate the figures the given number of degrees about the origin.  Label all points.  Find vertices 
                                                                                                                 of transformed image. 
                                                                                       a)  270                                                                                                                                                                                                                                                                                                                                                                              b) 180                                                                                                                                                                                                                                                                                                                                                                                c)  90 
                                                                               
                                                                            5)  Which statement describes the image: 
                                                                                                                 a)  Reflection in line  y 1 
                                                                                                                 b)  Reflection in line y  x 
                                                                                                                 c)  Rotation of 90 about origin 
                                                                                                                 d)  Rotation of 180about origin 
                                                                                                                 e)  Translation right 3 units, down 3 units 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
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                                                                            6)  How many lines of symmetry do the figures have?  Draw any you find on the figure and write the 
                                                                                                                 number. 
                                                                                       a)                                                                                                                                                                                                                               b)                                                                                                                                                                                                                              c)                                                                                                                                                                                                                                d)                                                                                                                                                                                                                               e)  
                                                                                                                                                                                                                                                                                       
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           
                                                                            7)  For each figure in the previous question, specify whether the figure has rotational symmetry.  If 
                                                                                                                 so, describe the degrees of rotation.  Does the figure have point symmetery?  If there is rotational 
                                                                                                                 symmetry, what is the order of the rotation? 
                                                                            8)  The vertices of quadrilateral ABCD are A(-3, 0), B(0, 6),  
                                                                                                                 C(3, 6), and D(3, 3).  Find the vertices of A’B’C’D’ after a 
                                                                                                                 dilation with scale factor 1 .  Graph the pre-image and the 
                                                                                                                                                                                                                                                                                                                                                                                                                 3
                                                                                                                 image, labeling all points.  Find vertices of transformed 
                                                                                                                 image. 
                                                                            9)  When printed, which of the digits 0 1 2 3 4 5 6 7 8 9 show line symmetry?  Which show point  
                                                                                 symmetry? 
                                                                            10) Using block printing, name the uppercase letters of the alphabet that show  
                                                                                                                 a)  vertical line symmetry  
                                                                                                                 b)  horizontal line symmetry 
                                                                                                                 c)  point symmetry