Happy Wednesday 

1. Happy Wednesday  • Pick up the paper from the front table. • Take out your homework and a red pen. • Take out your writing assignment. • Start writing down the learning objective on your guided notes • SWBAT translate figures by using vectors.

2. 12.2: Translations • Learning Objective • SWBAT translate figures by using vectors.

3. Math Joke of the Day! • French Woman: How did you get lost? Didn’t I tell you my office was one floor up and three doors down? • American Woman: I didn’t understand your translation!

4. Whiteboards: APK • What symbol do you use to write out the image? • The y-axis determines ( horizontal or vertical) shift. • The x-axis determines ( horizontal or vertical) shift.

5. 12.2: Translations On Monday, we discussed the basics of a Translation. I am going to call on two students using equity sticks and you are going to tell me one thing you know about a Translation. Translation– • a transformation where all the points of a figure are moved the same distance in the same direction.

6. Isometry • If I say that a translated image is isometric to it’s pre-image, what do you think I mean? • Think-pair-share • Isometry • image of a translated figure is congruentto the pre-image.

7. Example Non-Example

8. Introduction to TRANSLATIONS Slide 8

9. Translating a soccer ball By the end of the period, you are going to be able to translate this soccer ball by using vectors!

10. Example 1: Identifying Translations Tell whether each transformation appears to be a translation. Explain in 1-2 sentences. Fill this out on your guided notes. A. B. No; the figure appears to be flipped. Yes; the figure appears to slide.

11. Whiteboards Tell whether each transformation appears to be a translation. Be ready to share your answer. a. b. Yes; all of the points have moved the same distance in the same direction. No; not all of the points have moved the same distance.

12. When are we ever going to have to use this? • Computer animations • http://www.youtube.com/watch?v=dVtz55mIuz4 • 1:38- :3-19

13. Vectors • Show length and direction • Vectors in the coordinate plane can be written as <a, b> • a is the horizontalchange • b is the verticalchange • Think of it as (x,y)

14. CFU • What does the “a” represent? • What does the “b” represent?

15. Ex 2: Translations in the Coordinate Plane How did this image translate? • What are the coordinates for A, B, C? • What are the coordinates for A’, B’. C’? • How are they alike? • How are they different? Talk with your tablemates.

16. Example 2 Continued This is called a horizontal translation. Moved 6 units to the right. Rule: (x, y) ( x+a, y) (x, y) (x+6, y) Vector: < 6, 0>

17. Example 3: How did this image translate? • What are the coordinates for T, P, B? • What are the coordinates for T’, P’, B’? • How are they alike? • How are they different?

18. Example 3 Continued This is called a vertical translation. Moved 4 units up. Rule: (x, y) ( x, y+b) (x, y) (x, y+4) Vector: < 0, 4>

19. Example 4: Attempt on your own • Use arrow notation to show the relationship between the pre-images ordered pair and the images ordered pair. For example, A(2, 4)  A’(?, ?). • What do you notice about the x and y values of the pre-image and image? • Write a rule similar to Example 2 & 3. • Write a vector similar to Example 2 & 3. Discuss with your tablemates your solution. Do you all have the same idea? If not, provide evidence for your solution. On one whiteboard write your tables solution. Write legibly, random tables will be asked to share their whiteboard.

20. Example 4 Continued This is called a general translation (or diagonal translation) most commonly used… Think about the soccer ball! Moved 7 units to the left and 3 units down. Rule: (x, y) ( x+a, y+b) (x, y) (x-7, y-3) Vector: < -7, -3>

21. In Summary….

22. CFU • What happens to the x-value when there is a vertical translation? • Nothing! • What happens to the y-value when there is a horizontal translation? • Nothing! • What happens to the x and y-value when there is a diagonal translation? • Both move in a given direction

23. Let’s Go Back to the Soccer Ball!

24. Introduction to TRANSLATIONS Slide 24

25. Translating a soccer ball

26. 45 – 27 = 18+18m in y direction 65 – 10 = 55+55m in x direction Translating a football y 70 Vector notation (65,45) < 55, 18> (10,27) That’s a TRANSLATION of:+55m parallel to the x-axis and+18m parallel to the y-axis x 0 105

27. Translating a soccer ball y 70 (70,65) (60,50) (85,47) (107,37) (65,45) (93,39) (10,27) <55,18> < 14,-2> <10,15> <15,-18> < -5,5> < 8,-8> x 0 105

28. Example 6: Drawing Translations in the Coordinate Plane Translate the triangle with vertices D(–3, –1), E(5, –3), and F(–2, –2) along the vector <3, –1>. • Think: What does the vector tell us? • What is the horizontal change? • What is the vertical change?

29. Translate the triangle with vertices D(–3, 1), E(3, –3), and F(–2, –2) along the vector <3, –1>. • Step 1: • Draw the pre-image with the given coordinates • Step 2: • Move each vertex 3 units to the right and 1 unit down.

30. Whiteboards Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1,–1), and U(3, 1) along the vector <–3, –2> • What is the horizontal change? • What is the vertical change?

31. Whiteboards Directions: Using the graphing whiteboard, graph the pre-image. Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1,–1), and U(3, 1) along the vector <–3, –2> Do not show me until I say “Go!” Do not erase your pre-image.

32. Whiteboards Directions: Using the graphing whiteboard, graph the image given your pre-image. Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1,–1), and U(3, 1) along the vector <–3, –2> Do not show me until I say “Go!”

33. R R’ S U S’ U’ T T’ Check your Work!

34. Marching Band! In a marching drill, it takes 8 steps to march 5 yards. A drummer starts 8 steps to the left and 8 steps up from the center of the field. She marches 16 steps to the right to her second position. Then she marches 24 steps down the field to her final position. What is the drummer’s final position?

35. What are the drummer’s starting coordinates? • What is her second position? • What is her final position? • What single translation vector moves her from the starting position to her final position?

36. What if…? Directions: Do this silently. I should not here any talking. Suppose another drummer started at the center of the field and marched the same direction. What would the drummer’s final position be? Now, share with your tablemates your final answer. Did you all do it the same way or differently? There are 2 different ways to solve the problem. Try to come up with all the ways and provide each way on a different white board. Be ready to share out!

37. What did you notice about those different ways?

38. Example 8: Write down the translation vector for the following: LJ JK LK Can you w rite down a translation vector for LM? Explain.

39. Whiteboards: CFU 1. Tell whether the transformation appears to be a translation. yes 2. Use your graph whiteboard. Translate the figure with the given vertices along the given vector. Label your pre-image and image. G(8, 2), H(–4, 5), I(3,–1); <–2, 0>

40. Whiteboards: CFU 3. A rook on a chessboard has coordinates (3, 4). The rook is moved up two spaces. Then it is moved three spaces to the left. a. What is the rook’s final position? (0 ,6) b. What single vector moves the rook from its starting position to its final position? <–3, 2>

41. Closure: • What is a translation? • If point A was at ( 2, 3) and point A’ was at (-4, 5) along what vector would you translate? • If the vector is < 4, -2> how is the image translated? • Why is it important to be able to translate an object?