Standards with the same topic and subject but for other grades
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.
A transformation of preimage point 𝐴 can be denoted as the image 𝐴’ (read as “𝐴 prime”).
A reflection is a transformation in which an image is formed by reflecting the preimage over a line called the line of reflection. Each point on the image is the same distance from the line of reflection as the corresponding point in the preimage.
A translation is a transformation in which an image is formed by moving every point on the preimage the same distance in the same direction.
A translation of a figure on a wallpaper pattern shows the same figure slid the same distance in the same direction; and
A dilation is a transformation in which an image is formed by enlarging or reducing the preimage proportionally by a scale factor from the center of dilation (limited to the origin in grade eight). A dilation of a figure and the original figure are similar. The center of dilation may or may not be on the preimage.