Holt CA Course 1 8-7Transformations Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Holt CA Course 1 8-7Transformations Warm Up (4, –6) (12, 27) (–6, 2) 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).

Holt CA Course 1 8-7Transformations 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

Holt CA Course 1 8-7Transformations Vocabulary transformation image translation reflection rotation

Holt CA Course 1 8-7Transformations 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.

Holt CA Course 1 8-7Transformations

Holt CA Course 1 8-7Transformations 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.It is a reflection. The figure slides along a straight line.

Holt CA Course 1 8-7Transformations The point that a figure rotates around may be on the figure or away from the figure. Helpful Hint

Holt CA Course 1 8-7Transformations Check It Out! Example 1 Identify each type of transformation. A. B. 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.

Holt CA Course 1 8-7Transformations 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.

Holt CA Course 1 8-7Transformations 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

Holt CA Course 1 8-7Transformations Check It Out! Example 2 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’

Holt CA Course 1 8-7Transformations Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image. A. x-axis Additional Example 3: Graphing Reflections on a Coordinate Plane 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).

Holt CA Course 1 8-7Transformations 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. The coordinates of the vertices of triangle A’D’C’ are A’(3, 1), D’(0, 0), C’( – 2, 2). Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image.

Holt CA Course 1 8-7Transformations Check It Out! Example 3 3 x y A B C 3 –3 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’B’C are A’(1, 0), B’(3, –3), C’(5, 0). A’ B’ C’ Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image. A. x-axis

Holt CA Course 1 8-7Transformations Check It Out! Example 3 A x y B C 3 3 –3 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’B’C are A’(0, 0), B’(–2, 3), C’(–2, –3). C’ B’ Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image. B. y-axis

Holt CA Course 1 8-7Transformations 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 x y A B C 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’ –3

Holt CA Course 1 8-7Transformations Triangle ABC has vertices A(–2, 0), B(0, 3), C(0, –3). Rotate ∆ABC 180° about the vertex A. Check It Out! Example 4 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 4 3 –4 B’ C’ A

Holt CA Course 1 8-7Transformations Lesson Quiz: Part I 1. Identify the transformation. (1, –4), (5, –4), (9, 4) 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?

Holt CA Course 1 8-7Transformations 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.