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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 Slide 2 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). Slide 3 Learn to recognize, describe, and show transformations. Course 2 8-10 Translations, Reflections, and Rotations Slide 4 Vocabulary transformation image translation reflection line of reflection rotation Insert Lesson Title Here Course 2 8-10 Translations, Reflections, and Rotations Slide 5 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 Slide 6 Translation The figure slides along a straight line without turning. Course 2 8-10 Translations, Reflections, and Rotations Types of Transformations Slide 7 Reflection The figure flips across a line of reflection, creating a mirror image. Course 2 8-10 Translations, Reflections, and Rotations Types of Transformations Slide 8 Rotation The figure turns around a fixed point. Course 2 8-10 Translations, Reflections, and Rotations Types of Transformations Slide 9 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. Slide 10 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 Slide 11 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 Slide 12 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 Slide 13 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 Slide 14 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). Slide 15 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). Slide 16 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 Slide 17 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 Slide 18 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