# Transformations: Translations, Reflections, and Rotations

Learn to recognize, describe, and demonstrate transformations including translations, reflections, and rotations. Understand the vocabulary behind transformation and how to apply it in geometric problems. Understand how translations "slide" objects a fixed distance and face in the same direction.

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## About Transformations: Translations, Reflections, and Rotations

PowerPoint presentation about 'Transformations: Translations, Reflections, and Rotations'. This presentation describes the topic on Learn to recognize, describe, and demonstrate transformations including translations, reflections, and rotations. Understand the vocabulary behind transformation and how to apply it in geometric problems. Understand how translations "slide" objects a fixed distance and face in the same direction.. The key topics included in this slideshow are . Download this presentation absolutely free.

## Presentation Transcript

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’’