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Chapter 12

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For each example, how would I get the first image to look like the second?

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What are these examples of?

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A transformation of a geometric figure is a change in its position, shape, or size. Types of transformations: reflection (flip), translation (slide), rotation (turn), dilation (shrink or grow) Preimage – original figure before the transformation Image – resulting figure after the transformation

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An isometry is a transformation in which the preimage and image are congruent. In other words, there is a change in position, but not shape or size. A reflection is an isometry in which the orientation of the object and its image are opposites.

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A reflection is an isometry in which the orientation of the object and its image are opposites.

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ABCD is an image of KLMN. What is the image of angle L? Which side corresponds to NK? Sometimes images are named as A’B’C’D’ with the ‘ (prime) signifying the difference between the image and pre-image.

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∆XYZ has vertices X(-2,3), Y(1,1), and Z(2,4). Draw ∆XYZ and its reflection image in the x-axis. Name using primes.

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∆XYZ has vertices X(-2,3), Y(1,1), and Z(2,4). Draw ∆XYZ and its reflection image in the line x=3. Name using new letters.

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A translation is an isometry that maps all points of a figure the same distance in the same direction. We describe translations using vectors

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Find the image of F under the translation.

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Find the vector that describes the translation H→I.

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Find the vector that describes the translation ∆ABC→ ∆A’B’C’.

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Draw the image of ∆ABC under the translation.

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To describe a rotation, you need three pieces of information: 1. center of rotation (a point on or off the figure) ON Off

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2. angle of rotation (positive number, 360 max.) 3. direction of rotation (clockwise or counterclockwise)

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Draw the image that results when ABC is rotated counterclockwise 270° around the origin.

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A composition of reflections in two parallel lines is a translation. two intersecting lines is a rotation. A glide reflection is the composition of a glide (translation) and a reflection in a line parallel to the glide vector.

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A figure has symmetry if there is an isometry that maps the figure onto itself. Three types of symmetry: Line symmetry (a.k.a. reflectional symmetry) Rotational symmetry – is its own image for some rotation that is less than or equal to 180° Point symmetry – has rotational symmetry of exactly 180°

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What kind of symmetry does each figure have? (could be multiple types)

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A tessellation is a repeating pattern of figures that completely covers a plane, without gaps or overlaps. All triangles and quadrilaterals tessellate.

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A regular polygon will tessellate a plane if the interior angle measure will divide into 360 evenly.

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A dilation is a transformation whose preimage and image are similar. It is generally not an isometry.

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Every dilation has a center and a scale factor. The scale factor describes the size change from the original figure to the image. The dilation is an enlargement if the scale factor n > 1. It is a reduction if the scale factor 0 < n < 1.

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The green circle is a dilation of the blue circle. Describe the dilation.

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∆ABC is a dilation of ∆DBC. Find the center and scale factor.

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The scale factor on a museum's floor plan is 1 : 200. The length and width on the drawing are 8 in. and 6 in. Find the actual dimensions in feet and inches.

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∆XYZ has coordinates X(3,1), Y(2,-4), and Z (-2,0). Find the image for a dilation with center (0,0) and scale factor 2.5.

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