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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

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
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
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.”
slide5
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>

slide6

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

slide7

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
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

dilations2
Dilations

proportional

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

same

dilations3
Dilations

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