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**Translations, Reflections, and Rotations**

Course 2 8-10 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.

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**Types of Transformations**

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

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**Types of Transformations**

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

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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.

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**Types of Transformations**

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

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

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**A proportional Shrinking or enlargement of a figure **

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

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**Additional Example 1: Identifying Types of Transformations**

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

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**Insert Lesson Title Here**

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

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**Insert Lesson Title Here**

Course 2 8-10 Translations, Reflections, and Rotations Insert Lesson Title Here Check It Out: Example 1 Identify each type of transformation. A B. x y x y 4 4 2 2 –4 –2 2 4 –4 –2 2 4 –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.

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**Additional Example 2: Graphing Transformations on a Coordinate Plane**

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

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**Insert Lesson Title Here**

Course 2 8-10 Translations, Reflections, and Rotations 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

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**Insert Lesson Title Here**

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

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**Additional Example 3: Graphing Reflections on a Coordinate Plane**

Course 2 8-10 Translations, Reflections, and Rotations 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

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**Additional Example 3 Continued**

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

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**Additional Example 3 Continued**

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

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**Insert Lesson Title Here**

Course 2 8-10 Translations, Reflections, and Rotations 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. x y The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites. B 3 C A A’ B’ C’ 3 The coordinates of the vertices of triangle ABC are A’(1, 0), B’(3, –3), C’(5, 0). –3

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**Insert Lesson Title Here**

Course 2 8-10 Translations, Reflections, and Rotations 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. x y B C 3 –3 The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites. C’ B’ A The coordinates of the vertices of triangle ABC are A’(0, 0), B’(–2, 3), C’(–2, –3).

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**Additional Example 4: Graphing Rotations on a Coordinate Plane**

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

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**Translations, Reflections, and Rotations**

Course 2 8-10 Translations, Reflections, and Rotations 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. x y B The corresponding sides, AB and AB’ make a 180° angle. B’ C’ 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

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**Insert Lesson Title Here**

Course 2 8-10 Translations, Reflections, and Rotations Insert Lesson Title Here Lesson Quiz: Part I 1. Identify the transformation. reflection 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)

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**Insert Lesson Title Here**

Course 2 8-10 Translations, Reflections, and Rotations 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. x y 2 –2 –4 4 C C’ B’ A’ B A C’’ A’’ B’’

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