In mathematics, a transformation changes the position or orientation of a

1. 8-10 Translations, Reflections, and Rotations Course 2 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.

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

3. 8-10 Translations, Reflections, and Rotations Course 2 Types of Transformations Reflection The figure flips across a line of reflection, creating a mirror image.

4. Reflection Line is a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image.

5. 8-10 Translations, Reflections, and Rotations Course 2 Types of Transformations Rotation The figure turns around a fixed point.

6. Angle of Rotation The measure of degrees that a figure is rotated around a fixed point

7. Dilation: A proportional Shrinking or enlargement of a figure Under 1 will get smaller over 1 will get bigger

8. 8-10 Translations, Reflections, and Rotations Course 2 Additional Example 1: Identifying Types of Transformations Identify each type of transformation. B. A. The figure flips across the y-axis. The figure slides along a straight line. It is a reflection. It is a translation.

9. 8-10 Translations, Reflections, and Rotations Helpful Hint The point that a figure rotates around may be on the figure or away from the figure. Course 2 Insert Lesson Title Here

10. 8-10 Translations, Reflections, and Rotations y y x x Course 2 Insert Lesson Title Here Check It Out: Example 1 Identify each type of transformation. A. B. 4 4 2 2 4 4 0 0 –4 –4 –2 2 –2 2 –2 –2 –4 –4 The figure slides along a straight line. The figure turns around a fixed point. It is a translation. It is a rotation.

11. 8-10 Translations, Reflections, and Rotations Course 2 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.

12. 8-10 Translations, Reflections, and Rotations Course 2 Insert Lesson Title Here Reading Math A’ is read “A prime” and is used to represent the point on the image that corresponds to point A of the original figure

13. 8-10 Translations, Reflections, and Rotations y B’ A’ x C’ D’ Course 2 Insert Lesson Title Here Check It Out: Example 2 Translate quadrilateral ABCD 5 units left and 3 units down. B A 4 Each vertex is moved five units left and three units down. 2 C D 4 –4 –2 2 –2 –4

14. 8-10 Translations, Reflections, and Rotations Course 2 Additional Example 3: Graphing Reflections on a Coordinate Plane Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image. x-axis, then y-axis

15. 8-10 Translations, Reflections, and Rotations Course 2 Additional Example 3 Continued A. x-axis. 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 ADC are A’(–3, –1), D’(0, 0), C’(2, –2).

16. 8-10 Translations, Reflections, and Rotations Course 2 Additional Example 3 Continued B. y-axis. 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 ADC are A’(3, 1), D’(0, 0), C’(–2, 2).

17. 8-10 Translations, Reflections, and Rotations y x A’ C’ B’ Course 2 Insert Lesson Title Here Check It Out: Example 3A 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. B 3 C A 3 The coordinates of the vertices of triangle ABC are A’(1, 0), B’(3, –3), C’(5, 0). –3

18. 8-10 Translations, Reflections, and Rotations y B’ B 3 x 3 C’ –3 C Course 2 Insert Lesson Title Here Check It Out: Example 3B 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. A The coordinates of the vertices of triangle ABC are A’(0, 0), B’(–2, 3), C’(–2, –3).

19. 8-10 Translations, Reflections, and Rotations y The corresponding sides, AC and AC’ make a 180° angle. B 3 x C’ A’ C A B’ –3 Course 2 Additional Example 4: Graphing Rotations on a Coordinate Plane Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° about the vertex A. 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.

20. 8-10 Translations, Reflections, and Rotations y C’ The corresponding sides, AB and AB’ make a 180° angle. x B’ Course 2 Check It Out: Example 4 Triangle ABC has vertices A(0, –2), B(0, 3), C(0, –3). Rotate ∆ABC 180° about the vertex A. B 3 A 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. 3 –3 C

21. 8-10 Translations, Reflections, and Rotations Course 2 Insert Lesson Title Here Lesson Quiz: Part I reflection 1. Identify the transformation. 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? (1, –4), (5, –4), (9, 4)

22. 8-10 Translations, Reflections, and Rotations y 4 x 2 A’’ A’ C’’ C’ –4 –2 2 4 –2 B’’ B’ –4 Course 2 Insert Lesson Title Here 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. C A B