When you are on an amusement park ride, you are undergoing a transformation. A transformation is a change in a figure’s position or size. Translations, rotations, and reflections are types of transformations. The resulting figure, or image, of a translation, rotation, or reflection is congruent to the original figure. A translation slides a figure along a line without turning.

Additional Example 1: Graphing Translations on a Coordinate Plane Graph the translation of triangle ABC 2 units right and 3 units down. Add 2 to the x-coordinate of each vertex, and subtract 3 from the y-coordinate of each vertex. A’ B’ C’ Rule Image A(–3, 4)A’ (–3 + 2, 4 – 3) A’(–1, 1) B(0, 2)B’ (0 + 2, 2 – 3) B’(2, –1) C(–2, 1)C’ (–2 + 2, 1 – 3) C’(0, –2)

Check It Out: Example 1 Graph the translation of the quadrilateral ABCD 3 units down and 5 units left. Subtract 5 from the x-coordinate of each vertex, and subtract 3 from the y-coordinate of each vertex. A’ B’ Rule Image A(1, 4)A’ (1 – 5, 4 – 3) A’(–4, 1) B(4, 3)B’ (4 – 5, 3 – 3) B’(–1, 0) C(4, –1)C’ (4 – 5, –1 – 3) C’(–1, –4) C(1, –2)D’ (1 – 5, –2 – 3) D’(–4, –5) C’ D’ 4

A reflection flips a figure across a line to create a mirror image. 5

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Additional Example 2: Graphing Reflections on a Coordinate Plane Graph the reflection of quadrilateral ABCD across the y-axis. B’ A’ Multiply the x-coordinate of each vertex by –1. C’ Rule Image A(–4, 1)A’ (–1  –4, 1) A’(4, 1) B(–2, 1)B’ (–1  –2, 1) B’(2, 1) C(–1, –2)C’ (–1  –1, –2) C’(1, –2) D(–4, –3)D’ (–1  –4, –3) D’(4, –3) D’ 7

Graph the reflection of triangle FGH across the x-axis. Check It Out: Example 2 Graph the reflection of triangle FGH across the x-axis. Multiply the y-coordinate of each vertex by –1. H’ G’ F’ Rule Image F(–4, –2)F’ (–4, –2  –1) F’(–4, 2) G(1, –3) G’ (1, –3  –1) G’(1, 3) H(–2, –4)H’ (–2, –4  –1) H’(–2, 4) 8

A rotation turns a figure around a point, called the center of rotation. 9

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Additional Example 3: Graphing Rotations on a Coordinate Plane Graph the rotation of triangle ABC 90 counterclockwise about the origin. Multiply the y-coordinate of each vertex by –1, and switch the x and y coordinates. A’ B’ C’ Rule Image A(4, 4)A’ (–1  4, 4 ) A’(–4, 4) B(4, 1)B’ (–1  1, 4) B’(–1, 4) C(2, 1)C’ (–1  1, 2) C’(–1, 2) 11

Graph the rotation of triangle XYZ 180 about the origin. Check It Out: Example 3 Graph the rotation of triangle XYZ 180 about the origin. Multiply the both coordinates by –1. Rule Image X(–1, 2)X’ (–1  –1, –1  2 ) X’(1, –2) Y(2, 3)Y’ (–1  2, –1  3) Y’(–2, –3) Z(3, 0)Z’ (–1  3, –1  0) Z’(–3, 0) Z’ X’ Y’ 12

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 13

Lesson Quiz Graph each transformation of triangle ABC. 1. translation 4 units down 2. reflection across the y-axis 3. rotation of 180 about the origin

Lesson Quiz for Student Response Systems 1. Give the coordinates of (1, 4) after a translation 3 units up. A. (4, 4) B. (4, 7) C. (–4, –4) D. (–4, –7) 15

Lesson Quiz for Student Response Systems 2. Give the coordinates of (1, 4) after a reflection across the x-axis. A. (1, 4) B. (–1, –4) C. (1, –4) D. (–1, 4) 16 16

Lesson Quiz for Student Response Systems 3. Give the coordinates of (1, 4) after a 90 clockwise rotation around the origin. A. (4, 1) B. (4, –1) C. (1, –4) D. (–4, 1) 17 17