The preimage of a figure that has been translated and then reflected over the 𝑥- or 𝑦-axis may result in a different transformation than the preimage of a figure that has been reflected over the 𝑥- or 𝑦-axis and then translated.
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The result of first translating and then reflecting over the 𝑥- or 𝑦-axis may not result in the same transformation of reflecting over the 𝑥- or 𝑦-axis and then translating.
Sketch the image of a dilation of a right triangle or a rectangle limited to a scale factor of 1/4, 1/2, 2, 3, or 4. The center of the dilation will be the origin. (a)
The student will a) given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane; and b) identify practical applications of transformations.
Translations and reflections maintain congruence between the preimage and image but change location. Dilations by a scale factor other than 1 produce an image that is not congruent to the preimage but is similar. Reflections change the orientation of the image.
A transformation of a figure, called preimage, changes the size, shape, and/or position of the figure to a new figure, called the image.