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

Warm Up (4, –6) (12, 27) (–6, 2) Course 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).

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 Translations, Reflections, and Rotations

Learn to recognize, describe, and show transformations. Course Translations, Reflections, and Rotations

Vocabulary transformation image translation reflection line of reflection rotation Insert Lesson Title Here Course Translations, Reflections, and Rotations

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 Translations, Reflections, and Rotations

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

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

Rotation The figure turns around a fixed point. Course Translations, Reflections, and Rotations Types of Transformations

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 Translations, Reflections, and Rotations It is a reflection. The figure slides along a straight line.

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

Check It Out: Example 1 Identify each type of transformation. A. B. Insert Lesson Title Here Course 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.

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 Translations, Reflections, and Rotations

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 Translations, Reflections, and Rotations

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 Translations, Reflections, and Rotations

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 Translations, Reflections, and Rotations

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 Translations, Reflections, and Rotations The coordinates of the vertices of triangle ADC are A’( – 3, – 1), D’(0, 0), C’(2, – 2).

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 Translations, Reflections, and Rotations The coordinates of the vertices of triangle ADC are A’(3, 1), D’(0, 0), C’( – 2, 2).

Check It Out: Example 3A Insert Lesson Title Here 3 x y A B C 3 –3 Course 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’

Check It Out: Example 3B Insert Lesson Title Here A x y B C 3 3 –3 Course 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’

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 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’

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 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

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 Translations, Reflections, and Rotations

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 Translations, Reflections, and Rotations x y 2 –2 2 –4 4 4 C B A C’ B’ A’ C’’ A’’ B’’