Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up 1. Subtract 3 from the x-coordinate and 2 from the y-coordinate in (7, –4). (4, –6)‏ 2. Multiply each coordinate by 3 in (4, 9). (12, 27)‏ 3. Subtract 4 from the x-coordinate and add 3 to the to the y-coordinate in (–2, –1). (–6, 2)‏

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

Sunshine State Standards MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane. Also MA.7.G.4.3

Vocabulary transformation image preimage translation reflection line of reflection rotation

In mathematics, a transformation changes the position or orientation of a figure. The resulting figure is the image of the original figure, called the preimage. Images resulting from the transformations described in the next slides are congruent to the original figures.

Types of Transformations Translation The figure slides along a straight line without turning.

Types of Transformations Reflection The figure flips across a line of reflection, creating a mirror image.

Types of Transformations Rotation The figure turns around a fixed point.

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.

Check It Out: Example 1 Identify the type of transformation. translation

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.

Additional Example 2 Continued Write the coordinate of the vertices of the image. Quadrilateral ABCD (x – 4, y – 2) A’B’C’D’ A(1, 3) (1 – 4, 3 – 2) A’(–3, 1) B(4, 4) (4 – 4, 4 – 2) B’(0, 2) C(4, 1) (4 – 4, 1 – 2) C’(0, –1) D(1, –1) (1 – 4, –1 – 2) D’(–3, –3) The coordinates of the vertices of quadrilateral A'B'C'D' are A'(–3, 1), B'(0, 2), C'(0, –1), and D'(–3, –3).

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

Check It Out: Example 2 Graph the translation of quadrilateral ABCD 5 units left and 3 units down. x y A B C 2 –2 –4 4 D D’ C’ B’ A’

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.

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 A’D’C’ are A’(–3, –1), D’(0, 0), and C’(2, –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 A’D’C’ are A’(3, 1), D’(0, 0), and C’(–2, 2).

Check It Out: Example 3 Graph the reflection of quadrilateral ABCD across the x-axis.

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 origin. Write the coordinates of the vertices of the image. 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’ The coordinates of the vertices of triangle A’B’C’ are A’(0, 0), B’(–2, –3), and C’(–4, 0).

Check It Out: Example 4 Rotate the graph of quadrilateral ABCD 90° clockwise about the origin.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz 1. Identify the transformation. reflection 2. The figure formed by (–5, –6), (–1, –6), and (3, 2) is translated 6 units right and 2 units up. What are the coordinates of the new figure? (1, –4), (5, –4), (9, 4)‏ 3. Graph the triangle with vertices A(0, 0), B(–3, 0), C(–1, 4). Reflect ∆ABC across the y-axis and give the coordinates of the vertices of the image. A'(0, 0), B'(3, 0), C'(1, 4)‏

Lesson Quiz for Student Response Systems 1. Identify the transformation. A. translation B. reflection C. rotation D. none

Lesson Quiz for Student Response Systems 2. The figure formed by (–3, 2), (–4, 1), and (–1, –5) is translated 3 units right and 5 units up. What are the coordinates of the new figure? A. (–6, –3), (–7, –4), (–4, –10) B. (0, 7), (–7, –4), (2, –10) C. (0, 7), (–1, 6), (2, 0) D. (–6, –3), (–1, 6), (–4, 0)