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Solutions to the Symmetry WS

Solutions to the Symmetry WS. SIDE 1. SIDE 2. 1. a 2. b 3. a 4. c 5. a. 6. c 7 . b 8 . a 9 . c 10. a. 1. yes 2. 2 3. 8 4. 4 5. No 6. 4. Translations (Slide). We are learning to…identify and translate images on a coordinate plane.

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Solutions to the Symmetry WS

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  1. Solutions to the Symmetry WS SIDE 1 SIDE 2 1. a 2. b 3. a 4. c 5. a 6. c 7. b 8. a 9. c 10. a 1. yes 2. 2 3. 8 4. 4 5. No 6. 4

  2. Translations (Slide) We are learning to…identify and translate images on a coordinate plane. Homework: WS – Translations in the Coordinate Plane

  3. Translations on the Coordinate Plane

  4. Translations on theCoordinate Plane • In chess, there are rules governing how many spaces and in what direction each game piece can be moved • The diagram below shows the legal moves of the piece known as the knight

  5. A translation is a transformation of the plane that slides every point of a figure the same distance in the same direction. preimage The original object (preimage) and its translation (image) have the same shape and size, and they face in the same direction. image A translation is a rigid isometry. Isometry – transformation that maintains size and shape.

  6. There are several ways to indicate that a translation is to occur: 1. Description (verbal): 7 units to the left and 3 units down. 2. Mapping: (x, y)  (x -7, y – 3) 3. Notation: This may also be seen as T-7,-3( x, y) = (x -7, y - 3). In this example: each of these sets of directions indicated that you are to move each point in the preimage 7 units left then 3 units down.

  7. Example: the "slide" (translation) moves the figure7 units to the left and 3 units down. Quad ABCD is the preimage Quad A’B’C’D’ is the image A (2,4)  A’ (-5,1) B (4,4)  B’ (-3,1) C (5,2)  C’ (-2,-1) D (2,1)  D’ (-5,-2)

  8. Use the given rule to translate the figure. Then describe the transformation. Rule: (x, y+3) image Add 3 to the y’s. preimage Preimage Image (1,3) (1, 6) (1,1) (1, 4) (4,1) (4, 4) translated figure up 3 units

  9. Use the given rule to translatethe figure. Then describe the transformation. Rule: (x-2, y) Subtract 2 from x’s Preimage Image (-3,-2) (-5, -2) preimage (-3,-4) (-5, -4) image (0,-4) (-2, -4) translated figure left 2 units

  10. Summary of Translations Translates RIGHT Add to x Subtract from x Translates LEFT Add to y Translates UP Translates DOWN Subtract from y

  11. Translations in the Coordinate Plane: In the example below, notice how each vertex moves the same distance in the same direction. Translation notation image preimage

  12. Explain how to translate an image with the following directions: Slide the figure 4 units right, and 2 units up. Slide the figure 6 units left, and 15 units up. Slide the figure 12 units right, and 5 units down. Slide the figure 8 units left, and 10 units down.

  13. Write the following in translation notation: (x + 4, y + 5) (x - 9, y + 6) (x - 10, y– 13) (x + 2, y– 3)

  14. Translate the figure using the following directions: (x + 3, y – 7). Find the coordinates of the translated image: A′:___________________ B′:___________________ C′:___________________ D′:___________________ B (-4, -4) C A (1, 1) B ′ D C ′ (6, -1) A′ (5, -6) D ′

  15. Translate the figure using the following directions: Find the coordinates of the translated image: A′:___________________ B′:___________________ C′:___________________ (0, -3) C ′ B ′ (-4, 4) C B (4, 5) A ′ A

  16. http://www.teachertube.com/viewVideo.php?video_id=172666 http://www.teachbuzz.com/lessons/transformations-coordinate-plane http://www.virtualnerd.com/middle-math/integers-coordinate-plane/transformations http://www.misterteacher.com/alphabetgeometry/transformations.html#Slide

  17. Write the coordinate of the vertices of the image. The coordinates of the vertices of quadrilateral A'B'C'D' are A'(–3, 1), B'(0, 2), C'(0, –1), and D'(–3, –3).

  18. Use the given rule to translate the figure. Then describe the transformation. Rule: (x, y+3) Add 3 to the y’s. Preimage Image (1,3) (1, 6) (1,1) (1, 4) (4, 4) (4,1) translated figure up 3 units

  19. Use the given rule to translate the figure. Then describe the transformation. Rule: (x+5, y) Add 5 to the x’s. Preimage Image (-4,3) (1, 3) (-4,1) (1, 1) (-1,1) (4, 1) translated figure right 5 units

  20. Describe each transformation. (x+10, y) (x–5, y) (x, y+7) (x, y–6) (x+3,y–7) (x–4,y–5) (x–8,y+9) translates right 10 translates left 5 translates up 7 translates down 6 translates right 3 and down 7 translates left 4 and down 5 translates left 8 and up 9

  21. http://www.teachertube.com/viewVideo.php?video_id=172666 http://www.teachbuzz.com/lessons/transformations-coordinate-plane http://www.virtualnerd.com/middle-math/integers-coordinate-plane/transformations http://www.misterteacher.com/alphabetgeometry/transformations.html#Slide

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