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Learn to recognize, describe, and show transformations. Course 2 8-10 Translations, Reflections, and Rotations

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Vocabulary transformation image translation reflection line of reflection rotation Insert Lesson Title Here Course 2 8-10 Translations, Reflections, and Rotations

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A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction. The word "translate" in Latin means "carried across".

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Think of polygon ABCDE as sliding two inches to the right and one inch down. Its new position is labeled A'B'C'D'E'. A translation moves an object without changing its size or shape and without turning it or flipping it.

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Remember: Translations are SLIDES!!!

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A reflection can be seen in water, in a mirror, in glass, or in a shiny surface. An object and its reflection have the same shape and size, but the figures face in opposite directions. In a mirror, for example, right and left are switched.

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The line (where a mirror may be placed) is called the line of reflection. The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection. A reflection can be thought of as a "flipping" of an object over the line of reflection. Remember: Reflections are FLIPS!!!

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A rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures may be turned in different directions.

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Remember: Rotations are TURNS!!! This rotation is 90 degrees counterclo ckwise.

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Identify each type of transformation. Additional Example 1: Identifying Types of Transformations The figure flips across the y-axis. A. B. It is a translation. Course 2 8-10 Translations, Reflections, and Rotations It is a reflection. The figure slides along a straight line.

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Insert Lesson Title Here Course 2 8-10 Translations, Reflections, and Rotations The point that a figure rotates around may be on the figure or away from the figure. Helpful Hint

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Check It Out: Example 1 Identify each type of transformation. A. B. Insert Lesson Title Here Course 2 8-10 Translations, Reflections, and Rotations x y 2 2 –2 –4 4 4 –2 0 x y 2 2 –4 4 4 –2 0 It is a translation. The figure slides along a straight line. It is a rotation. The figure turns around a fixed point.

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Additional Example 2: Graphing Transformations on a Coordinate Plane Graph the translation of quadrilateral ABCD 4 units left and 2 units down. Each vertex is moved 4 units left and 2 units down. Course 2 8-10 Translations, Reflections, and Rotations

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Insert Lesson Title Here A’ is read “A prime” and is used to represent the point on the image that corresponds to point A of the original figure Reading Math Course 2 8-10 Translations, Reflections, and Rotations

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Check It Out: Example 2 Insert Lesson Title Here Translate quadrilateral ABCD 5 units left and 3 units down. Each vertex is moved five units left and three units down. x y A B C 2 2 –2 –4 4 4 –2 D D’ C’ B’ A’ Course 2 8-10 Translations, Reflections, and Rotations

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Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image. x-axis, then y-axis Additional Example 3: Graphing Reflections on a Coordinate Plane Course 2 8-10 Translations, Reflections, and Rotations

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A. x-axis. Additional Example 3 Continued The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites. Course 2 8-10 Translations, Reflections, and Rotations The coordinates of the vertices of triangle ADC are A’( – 3, – 1), D’(0, 0), C’(2, – 2).

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B. y-axis. Additional Example 3 Continued The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites. Course 2 8-10 Translations, Reflections, and Rotations The coordinates of the vertices of triangle ADC are A’(3, 1), D’(0, 0), C’( – 2, 2).

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Check It Out: Example 3A Insert Lesson Title Here 3 x y A B C 3 –3 Course 2 8-10 Translations, Reflections, and Rotations Graph the reflection of the triangle ABC across the x-axis. Write the coordinates of the vertices of the image. The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites. The coordinates of the vertices of triangle ABC are A’(1, 0), B’(3, –3), C’(5, 0). A’ B’ C’

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Check It Out: Example 3B Insert Lesson Title Here A x y B C 3 3 –3 Course 2 8-10 Translations, Reflections, and Rotations Graph the reflection of the triangle ABC across the y-axis. Write the coordinates of the vertices of the image. The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites. The coordinates of the vertices of triangle ABC are A’(0, 0), B’(–2, 3), C’(–2, –3). C’ B’

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Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° about the vertex A. Additional Example 4: Graphing Rotations on a Coordinate Plane Course 2 8-10 Translations, Reflections, and Rotations x y A B C 3 –3 The corresponding sides, AC and AC’ make a 180° angle. Notice that vertex C is 4 units to the right of vertex A, and vertex C’ is 4 units to the left of vertex A. C’ B’ A’

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Triangle ABC has vertices A(0, –2), B(0, 3), C(0, –3). Rotate ∆ABC 180° about the vertex A. Check It Out: Example 4 Course 2 8-10 Translations, Reflections, and Rotations The corresponding sides, AB and AB’ make a 180° angle. Notice that vertex B is 2 units to the right and 3 units above vertex A, and vertex B’ is 2 units to the left and 3 units below vertex A. x y B C 3 3 –3 B’ C’ A

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Lesson Quiz: Part I 1. Identify the transformation. (1, –4), (5, –4), (9, 4) reflection Insert Lesson Title Here 2. The figure formed by (–5, –6), (–1, –6), and (3, 2) is transformed 6 units right and 2 units up. What are the coordinates of the new figure? Course 2 8-10 Translations, Reflections, and Rotations

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Lesson Quiz: Part II 3. Graph the triangle with vertices A(–1, 0), B(–3, 0), C(–1, 4). Rotate ∆ABC 90° counterclockwise around vertex B and reflect the resulting image across the y-axis. Insert Lesson Title Here Course 2 8-10 Translations, Reflections, and Rotations x y 2 –2 2 –4 4 4 C B A C’ B’ A’ C’’ A’’ B’’

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