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Geometry. Lesson 6.2a – Transformations: Translations and Dilations. CGT.5.G.5 Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane translations reflections
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Geometry Lesson 6.2a – Transformations: Translations and Dilations • CGT.5.G.5 Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane • translations • reflections • rotations (90˚, 180˚, clockwise and counterclockwise about the origin) • dilations (scale factor)
Transformations • Transformation:a change in position, shape, size, or orientation. • A transformation describes, or maps a change from one figure to another. • The original figure is a pre-image. • The resulting figure is an image.
Translations • A translation is a transformation that moves points in a coordinate plane the same distance and in the same direction. • A translation is often called a slide. • Vector notation <x, y> is used to represent the direction and distance of the translation. This notation is read “vector x, y.”
Use the given vector and figure to create a sketch of a three-dimensional figure.
Graph the triangle with the given vertices. Then graph the image of the triangle under the given translation. A (2,2) B (3, 4) C(2, -4) T: <x, y> <4 , - 3>
What is the image of A under the translation <1, 2>? • What is the image of A under the translation <3, -2>? • What vector describes the translation E D? • What vector describes the translation B E B D A C E
Find a single translation that has the same effect as each composition of translations. • <2, 5> followed by <-4, 9> • <-3, 7> followed by <1, -3>
Dilations • Figures are made larger or smaller by some amount called a ____________. • Dilations on the coordinate plane are centered on the _______. • Scale factors are ___________. • To scale a figure, multiply _____ its dimensions by the same factor. scale factor origin multipliers all
Dilations proportional • Similar figures are _________________. • All parts must grow or shrink by the ________ amount. same
Dilations Find the scale factor that maps the solid rhombus to the transparent rhombus.