Geometry

1. 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)

2. 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.

3. 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.”

4. Use the given vector and figure to create a sketch of a three-dimensional figure.

5. 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>

6. 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

7. 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>

8. 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

9. Dilations ⅓

10. Dilations proportional • Similar figures are _________________. • All parts must grow or shrink by the ________ amount. same

11. Dilations Find the scale factor that maps the solid rhombus to the transparent rhombus.

12. Dilations