MLS                                                                                                   Yolanda Volcimus
Harvard                                                                                                10/1/12


           A single transformation that can replace the combination of a reflection across the y-axis followed by a reflection across the y-axis is a 180 degrees counter-clockwise rotation. These translations are equivalent because they both have the same coordinates; same size and shape. A=(1,3), B=(2,1), and C=(1,1); A''=(-1,-3), B''=(-2,-1), and C''=(-1,-1). After performing the 180 degrees counter-clockwise, my coordinates were: A'=(-1,-3), B'=(-2,-1), and C'=(-1,-1). Knowing that two reflections are equivalent to one transformation can help me to remember the rule for the single transformation because I know that a reflection over the y-axis will get the image in the 3rd quadrant if the image was in the first quadrant. Also, a 180 degrees counter-clockwise rotation will get the image in the 3rd quadrant if the image was in the first quadrant. Thus, two transformations can be equivalent to one transformation.