Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 1

Plot the ordered pairs on the coordinate plane. Connect the points. Warm Up Plot the ordered pairs on the coordinate plane. Connect the points. 1. (3, 4) 2. (–5, 0)‏ 3. (–2, 0) 4. (–5, 4)‏ 5. name the polygon x y 4 2 -4 -2 2 4 -2 -4 trapezoid‏ 2

Which capital letters of the alphabet have line symmetry? Problem of the Day Which capital letters of the alphabet have line symmetry? A, B, C, D, E, H, I, K, M, O, T, U, V, W, X, Y 3

Learn to use translations, reflections, and rotations to change the positions of figures in the coordinate plane. 4

Additional Example 1: Translating Figures in the Coordinate Plane Translate rectangle ABCD 4 units left. Give the coordinates of each vertex in the image. x y Each vertex is translated 4 units right. 4 A’ B’ C’ D’ A B C D 2 The vertices of the image are A’(–3, 2), B’(–1, 2), C’(–3, 1), and D'(–1, 1).‏ –4 –2 2 4 –2 –4 5

A' is read “A prime.” Prime notation is used to represent the point on the image that corresponds to the same point on the original figure. Reading Math 6

Each vertex is translated 5 units right. Check It Out: Example 1 Translate square ABCD 5 units right. Give the coordinates of each vertex in the image. x y Each vertex is translated 5 units right. 4 2 The vertices of the image are A’(–4, 1), B’(–1, 1), C’(–4, –4), and D'(–1, –4).‏ –4 –2 2 4 A B A' B' C' D' –2 C D 7

Additional Example 2: Reflecting Figures in the Coordinate Plane Reflect triangle RST across the y-axis. Give the coordinates of each vertex in the image. x y Each vertex of the image is the same distance from the y-axis as the corresponding vertex in the original figure. 4 S T’ R’ S’ The vertices of the image are R’(–1, 0), S’(–2, 2), and T’(–2, –2). R 4 T –4 8

A line of reflection is not limited to the x-axis or y-axis A line of reflection is not limited to the x-axis or y-axis. Any line can be a line of reflection. Helpful Hint 9

Check It Out: Example 2 Reflect triangle ABC across the x-axis. Give the coordinates of each vertex in the image. x y Each vertex of the image is the same distance from the y-axis as the corresponding vertex in the original figure. B 3 A C A’ B’ C’ The vertices of the image are A’(1, 0), B’(3, –3), and C’(5, 0). –3 10

Additional Example 3: Rotating Figures in the Coordinate Plane Rotate triangle JKL 90° counter-clockwise about the origin. Give the coordinates of each vertex in the image. x y Notice that the vertex K is 3 units to the right of the origin, and vertex K is 3 units above the origin. Similarly, vertex L is 1 unit to the right of the origin, and vertex L' is 1 unit above the origin. K' J' L' J 2 –2 L 2 K –2 The vertices of the image are J’(–2, 2), K’(0, 3), and L’(0, 1). 11

Notice that the vertex D’ remains on the origin. Check It Out: Example 3 Rotate triangle JKL 180° counter-clockwise about the origin. Give the coordinates of each vertex in the image. Notice that the vertex D’ remains on the origin. The vertices of the triangle are ADC are A’(–3, –1), D’(0, 0), and C’(2, –2). 12

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

Lesson Quiz 1. Translate triangle DEF down 5 units. Give the coordinates of each vertex in the image. D’(1, –1), E’(3, –3), F’(2, –4) 2. Reflect triangle DEF across the y-axis. Give the coordinates of each vertex in the image. D’(– 1, 4), E’(– 3, 2), F’(– 2, 1) 3. Rotate triangle DEF 90 clockwise around the origin. Give the coordinates of each vertex in the image. D’(4, –1), E’(2, –3), F’(1, –2) 14

Lesson Quiz for Student Response Systems 1. Describe the transformation. A. translation 3 units up B. translation 3 units down C. reflection 3 units down D. reflection 3 units up 15

Lesson Quiz for Student Response Systems 2. Give the coordinates of each vertex after translated 2 units down. A. A’(–4, 2), B’(–2, 2), C’(–3, 1) B. A’(–4, 2), B’(–2, 2), C’(–3, –1) C. A’(4, 2), B’(2, 2), C’(–3, 1) D. A’(4, 2), B’(2, 2), C’(3, 1) 16

Lesson Quiz for Student Response Systems 3. Give the coordinates of each vertex after reflected across the y-axis. A. A’(4, –4), B’(2, –4), C’(3, –1) B. A’(–4, –4), B’(–2, –4), C’(–3, –1) C. A’(4, 4), B’(2, 4), C’(–3, 1) D. A’(4, 4), B’(2, 4), C’(3, 1) 17