Download Transformational Geometry Notes

Math 2 Transformational Geometry Notes Name ______________________________________ Date ________________ 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). Dilations • A dilation is 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 For the preimage point (𝑥, 𝑦): Rigid Transformations Non-­‐rigid Reflections Rotations Dilations Translations Clockwise Counterclockwise (𝒙 + 𝒉, 𝒚 + 𝒌) About x-­‐axis: About y-­‐axis: (negative angles) (𝑘𝑥, 𝑘𝑦) (positive angles) 90° (𝑥, −𝑦) (−𝑥, 𝑦) (−𝑦, 𝑥) −270° (−𝑦, 𝑥) −𝑥, −𝑦 −𝑥, −𝑦 180° −180° 𝑦, −𝑥 𝑦, −𝑥 270° −90°