Review of TransformationsHigh School Math based on the topics required for the Regents Exam conducted by NYSED.
A reflection is a flip. It is an opposite isometry. This means that the image does not change size but the lettering is reversed. Reflection in the x-axis: Rx-axis (x, y) = (x, –y) Reflection in the y-axis: Ry-axis(x, y) = (–x, y) Reflection in the line y = x: Ry = x(x, y) = (y, x) Reflection in the line y = -x, Ry = -x(x, y) = (–y, –x)
A rotation turns a figure through an angle about a fixed point called the center. A positive angle of rotation turns the figure counterclockwise, and a negative angle of rotation turns the figure in a clockwise direction. It is a direct isometry - the order of the lettering in the figure and the image are the same. Rotation of 90° about the origin: R90°(x, y) = (–y, x) Rotation of 180° (or point rotation about the origin) : R180°(x, y) = (–x, –y) Rotation of 270° about the origin : R270°(x, y) = (y, –x)
A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction. It is a direct isometry - the order of the lettering in the figure and the image are the same. Translation of h, k : Th,k(x, y) = (x+h, y+k)
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is not an isometry and it forms similar figures. Dilation of scale factor k with the center at the origin: Dk(x, y) = (kx, ky)
Custom Search
We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page. © Copyright 2005, 2009, 2010 - onlinemathlearning.com Embedded content, if any, are copyrights of their respective owners.
|
Custom Search