Preview Warm Up California Standards Lesson Presentation

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)

MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections. California Standards

Vocabulary transformation image translation reflection rotation

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.

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.

The point that a figure rotates around may be on the figure or away from the figure. Helpful Hint

Identify each type of transformation. A. B. 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.

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.

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.

Translate quadrilateral ABCD 5 units left and 3 units down. 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

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. 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), C’(2, –2).

Additional Example 3 Continued Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image. 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), C’(–2, 2).

Check It Out! Example 3 Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image. A. x-axis 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 A’B’C are A’(1, 0), B’(3, –3), C’(5, 0). –3

Check It Out! Example 3 Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image. B. y-axis 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 A’B’C are A’(0, 0), B’(–2, 3), C’(–2, –3).

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 The corresponding sides, AC and AC’ make a 180° angle. –3 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’

Triangle ABC has vertices A(–2, 0), B(0, 3), Check It Out! Example 4 Triangle ABC has vertices A(–2, 0), B(0, 3), C(0, –3). Rotate ∆ABC 180° about the vertex A. x y 4 B The corresponding sides, AB and AB’ make a 180° angle. B’ C’ 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 C –4

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)

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.