1. 8-10 Translations, Reflections, and Rotations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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).

3. Problem of the Day Some numbers appear as different numbers when rotated or reflected. Name as many as you can. Possible answers: 6 and 9; 6999 and 6669; IV and VI; IX and XI Course 2 8-10 Translations, Reflections, and Rotations

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

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

6. 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

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

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

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

10. 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.

11. 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

12. 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.

13. 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

14. 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

15. 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

16. 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

17. 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).

18. 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).

19. 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’

20. 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’

21. 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’

22. 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

23. 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

24. 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’’