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

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

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Translations on the Coordinate Plane

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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

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

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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) 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.

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Example: the "slide" (translation) moves the figure 7 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)

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Opposite Isometry - orientation is not preserved – the order of the lettering is reversed, either clockwise becomes counterclockwise or counterclockwise becomes clockwise. Isometry – size & shape are preserved - the figures are congruent. Direct Isometry - orientation is preserved – the order of the lettering in the figure the image are the same, either both clockwise or both counterclockwise.

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

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

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Summary of Translations Add to x Translates RIGHT Subtract from xTranslates LEFT Add to yTranslates UP Subtract from y Translates DOWN

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

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Explain how to translate an image with the following directions: Translation Mapping How should we translate this object? (x + 4, y + 2) (x – 6, y + 15) (x + 12, y – 5) (x – 8, y – 10) 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.

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Write the following in translation notation: Translation Directions Translation Notation Mapping “Translate a figure right 4 and up 5.” “Translate a figure left 9 and up 6.” “Translate a figure left 10 and down 13.” “Translate a figure right 2 and down 3.” (x + 4, y + 5) (x - 9, y + 6) (x - 10, y – 13) (x + 2, y – 3)

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

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B A B ′ C ′ Find the coordinates of the translated image: A ′:___________________ B ′:___________________ C ′:___________________ (-4, 4) (0, -3) (4, 5) C A ′

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

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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). Quadrilateral ABCD(x – 4, y – 2)A’B’C’D’ A(1, 3)(1 – 4, 3 – 2)A’(–3, 1) B(4, 4)(4 – 4, 4 – 2)B’(0, 2) C(4, 1)(4 – 4, 1 – 2)C’(0, –1) D(1, –1)(1 – 4, –1 – 2)D’(–3, –3)

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

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

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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

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

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