Transformations: Translations, Reflections, and Rotations

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

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

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

4. 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.

5. Remember: Translations are SLIDES!!! Translations are SLIDES!!!

6. 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.

7. 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!!!

8. 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.

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

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 –4 –2 0 x y 2 2 –2 –4 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 –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 –2 –4 –4 4 4 C B A C’ B’ A’ C’’ A’’ B’’