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Honors Geometry Transformations Section 3 Translations and Compositions A translation (or slide) is a transformation which maps every two points P and Q in the plane to points P and Q so that the following properties are true: 1. PP QQ 2. PP QQ The following coordinate notation can define translations in the coordinate plane: (x, y) ( x + a , y + b ) where a and b are constants. This notation shifts the point ________________ a units to the right and _________. b units up B D A D C ( X , Y ) ( X 1, Y 6) A composition results when two or more transformations are performed one after the other. Example 1: Sketch the image of AB after a composition of the given rotation and reflection. 2 -5 1 -2 B A 2 5 1 2 Reflection in the x-axis 90 clockwise about the origin A B While the order of the transformations affected the final image in the previous example, that is not the case with a glide reflection. A glide reflection is a composition of a translation and a reflection where the line of reflection is parallel to the direction of the translation. Example 3: Determine the coordinates of the image of A(4, -2) after the described composition. Is the composition a glide reflection? A 4,2 Yes, it is a glide reflection Example 4: Determine the coordinates of the image of A(4, -2) after the described composition. Is the composition a glide reflection? A A7,7 NO, it is not a glide reflection