1. Check 12-2 HW

2. Course 1 12-3 Graphing Translation 6 th Grade Math HOMEWORK Page 629 #14-16

3. Course 1 12-1 Tables and Functions Our Learning Goal Students will understand functions by creating tables and graphing translations.

4. Course 1 12-1 Tables and Functions Students will understand functions by creating tables and graphing translations. Learn to use data in a table to write an equation for a function and to use the equation to find a missing value. Learn to represent linear functions using ordered pairs and graphs. Learn to use translations to change the positions of figures on a coordinate plane. Learn to use reflections to change the positions of figures on a coordinate plane. Learn to use rotations to change positions of figures on a coordinate plane. Learn to visualize and show the results of stretching or shrinking a figure.

5. Today’s Learning Goal Assignment Learn to use translations to change the positions of figures on a coordinate plane. Course 1 12-3 Graphing Translation

6. 12-3 Graphing Translations Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

7. Warm Up 1. Use the given x-values to write solutions of the following equation as ordered pairs. y = 6x – 2 for x = 0, 1, 2, 3 2. Determine whether (3, –13) is a solution to the equation y = –4x – 1. (0, –2), (1, 4), (2, 10), (3, 16) yes Course 1 12-3 Graphing Translation

8. Problem of the Day Samantha’s house is 3 blocks east and 5 blocks south of Tyra. If Tyra walks straight south and then straight east to Samantha’s house, does she walk more blocks east or more blocks south? How many more? south; 2 blocks Course 1 12-3 Graphing Translation

9. A translation is a movement of a figure along a straight line. You can translate a figure on a coordinate plane by sliding it horizontally, vertically, or diagonally. Course 1 12-3 Graphing Translation

10. Additional Example 1: Translating Figures on a Coordinate Plane Give the coordinates of the vertices of the figure after the given translation. Translate triangle DEF 4 units left and 3 units up. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 6 5 4 3 2 1 -2 -3 -4 -5 -6 F D E y x Course 1 12-3 Graphing Translation

11. Additional Example 1 Continued To move the triangle 4 units left, subtract 4 from each of the x-coordinates. To move the triangle 3 units up, add 3 to each of the y-coordinates. DEFD’E’F’D’E’F’ D(1, 4) E(4, 2) F(–3, –3) D’(1 – 4, 4 + 3)D’(–3, 7) E’(0, 5) F’(–7, 0) E’(4 – 4, 2 + 3) F’(-3 – 4, –3 + 3) Course 1 12-3 Graphing Translation

12. Additional Example 1 Continued -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 5 4 3 1 -2 -3 -5 -6 6 2 -4 E’E’ F’F’ D’D’ y x F D E Course 1 12-3 Graphing Translation

13. Try This: Example 1 Give the coordinates of the vertices of the figure after the given translation. Translate triangle GHJ 3 units left and 3 units up. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 6 5 4 3 2 1 -2 -3 -4 -5 -6 J G H y x Course 1 12-3 Graphing Translation

14. Try This: Example 1 To move the triangle 3 units left, subtract 3 from each of the x-coordinates. To move the triangle 3 units up, add 3 to each of the y-coordinates. GHJG’H’J’ G(2, 4) H(4, 4) J(–3, –2) G’(2 – 3, 4 + 3)G’(–1, 7) H’(1, 7) J’(–6, 1) H’(4 – 3, 4 + 3) J’(–3 – 3, –2 + 3) Course 1 12-3 Graphing Translation

15. Try This: Example 1 Continued -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 5 4 3 1 -2 -3 -5 -6 6 2 -4 H’H’ J’J’ G’G’ y x J G H x Course 1 12-3 Graphing Translation

16. Additional Example 2: Music Application Members of a marching band begin in a trapezoid formation represented by trapezoid KLMN. Then they move 4 steps right and 5 steps down. Give the coordinates of the vertices of the trapezoid after such a translation. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 6 5 4 3 2 1 -2 -3 -4 -5 -6 M K L y x N -7 -8 Course 1 12-3 Graphing Translation

17. Additional Example 2 Continued To move 4 steps right, add 4 to each of the x-coordinates. To move 5 steps down, subtract 5 from each of the y-coordinates. KLMNK’L’M’N’ K(–2, 1) L(1, 1) M(3, –3) K’(–2 + 4, 1 – 5)K’(2, –4) L’(5, –4) M’(7, –8) L’(1 + 4, 1 – 5) M’(3 + 4, –3 – 5) N(–4, –3)N’(0, –8)M’(–4 + 4, –3 – 5) Course 1 12-3 Graphing Translation

18. Additional Example 2 Continued -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 6 5 4 3 2 1 -2 -3 -4 -5 -6 M K L y x N -7 M’M’ K’K’L’L’ N’N’ -8 x Course 1 12-3 Graphing Translation

19. Try This: Example 2 Members of a flag team begin in a trapezoid formation represented by trapezoid KLMN. Then they move 3 steps right and 2 steps down. Give the coordinates of the vertices of the trapezoid after such a translation. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 6 5 4 3 2 1 -2 -3 -4 -5 -6 M K L y x N Course 1 12-3 Graphing Translation

20. Try This: Example 2 To move 3 steps right, add 3 to each of the x-coordinates. To move 2 steps down, subtract 2 from each of the y-coordinates. KLMNK’L’M’N’ K(–1, 3) L(1, 3) M(3, –1) K’(–1 + 3, 3 – 2)K’(2, 1) L’(4, 1) M’(6, –3) L’(1 + 3, 3 – 2) M’(3 + 3, –1 – 2) N(–3, –1)N’(0, –3)M’(-3 + 3, –1 – 2) Course 1 12-3 Graphing Translation

21. Try This: Example 2 Continued -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 6 5 4 3 2 1 -2 -3 -4 -5 -6 M K L y N x M’ K’K’ L’L’ N’N’ Course 1 12-3 Graphing Translation

22. Lesson Quiz Give the coordinates of the vertices of triangle ABC, with vertices A(-5, -4), B(-3, 2), and C(1, -3), after the given translations. 1. Translate triangle ABC 3 units up and 2 units right. 2. Translate triangle ABC 5 units down and 3 units left. 3. Translate triangle ABC 2 units down and 4 units right. A’(-3, -1), B’(-1, 5), and C’(3,0) Insert Lesson Title Here A’(-8, -9), B’(-6, -3), and C’(-2,-8) A’(-1, -6), B’(1, 0), and C’(5,-5) Course 1 12-3 Graphing Translation