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Math II – Transformation Geometry Vocab Vocabulary: Preimage – the original figure in the transformation of a figure in a plane. Image – the new figure that results from the transformation of a figure in a plane. Isometry – a transformation that preserves size: preimage and image are congruent. Mapping – an operation that matches each element of a set with another element, its image, in the same set. Transformation – the operation that maps, or moves, a preimage onto an image. Three basic rigid transformations are reflections, rotations, and translations. A dilation is a non-rigid transformation (not an isometry). Translation – sliding a figure without changing the size or shape of figure Reflection – creates symmetry in the coordinate plane Dilations - a transformation that produces an image that is the same shape as the original, but is a different size (similar figure, so NOT an isometry) • Dilations are enlargements (“stretches”) or reductions (“shrinks”) • Scale factors are applied to the pre-image to create the image • We multiply points in the pre-image by the scale factor to create the image • Find scale factor by dividing a side length in the image by the corresponding side in the pre-image • Scale factors bigger than 1 result in enlargements • Scale factors smaller than 1 but greater than 0 result in reductions Rotation – turn a figure about a fixed point ** counterclockwise rotation ** Composite transformations – multiple transformations done on a figure ** first is on the pre-image, second is on the image, the third is on the second image. NEVER GO BACK TO THE ORIGINAL!! For the preimage point (𝑥, 𝑦): Translations (𝒙 + 𝒉, 𝒚 + 𝒌) Rigid Transformations Reflections Rotations About xAbout y-axis: Counterclockwise Clockwise axis: (positive angles) (negative angles) (𝑥, −𝑦) (−𝑥, 𝑦) 90° (−𝑦, 𝑥) −270° (−𝑦, 𝑥) About 𝑦 = 𝑥 About 𝑦 = −𝑥 180° −𝑥, −𝑦 180° −𝑥, −𝑦 (𝑦, −𝑥) (−𝑦, −𝑥) 270° 𝑦, −𝑥 −90° 𝑦, −𝑥 Non-rigid Dilations (𝑘𝑥, 𝑘𝑦)