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8-10 Translations, Reflections, and Rotations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Warm Up (4, –6) (12, 27) (–6, 2) Course 2 8-10 Translations, Reflections, and Rotations 1. Subtract 3 from the x-coordinate and 2 from the y-coordinate in (7, –4). 2. Multiply each coordinate by 3 in (4, 9). 3. Subtract 4 from the x-coordinate and add 3 to the to the y-coordinate in (–2, –1).

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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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In mathematics, a transformation changes the position or orientation of a figure. The resulting figure is the image of the original. Images resulting from the transformations described in the next slides are congruent to the original figures. Course 2 8-10 Translations, Reflections, and Rotations

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Translation The figure slides along a straight line without turning. Course 2 8-10 Translations, Reflections, and Rotations Types of Transformations

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Reflection The figure flips across a line of reflection, creating a mirror image. Course 2 8-10 Translations, Reflections, and Rotations Types of Transformations

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Rotation The figure turns around a fixed point. Course 2 8-10 Translations, Reflections, and Rotations Types of Transformations

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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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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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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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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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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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