Determine the rule described in the transformations below. a) Rigid Transformation/Isometry b) Translations

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  • Transformation Unit Review

    Name ____________________________________________ Period ___________ Date:_______________

    Determine the rule described in the transformations below.

    1. Which transformation has occurred to quadrilateral AHUP?

    a. π‘Ÿπ‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 90Β°

    b. π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘’π‘‘ π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  π‘₯ βˆ’ π‘Žπ‘₯𝑖𝑠

    c. π‘Ÿπ‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 180Β°

    d. π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘’π‘‘ π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  𝑦 βˆ’ π‘Žπ‘₯𝑖𝑠

    2. Which transformation has occurred to triangle UXS?

    a. π‘Ÿπ‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 90Β°

    b. π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘’π‘‘ π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  π‘₯ βˆ’ π‘Žπ‘₯𝑖𝑠

    c. π‘Ÿπ‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 180Β°

    d. π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘’π‘‘ π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  𝑦 βˆ’ π‘Žπ‘₯𝑖𝑠

    3. Which transformation has occurred to quadrilateral AKJI?

    a. π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘’π‘‘ π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  𝑦 = π‘₯

    b. π‘Ÿπ‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 270Β°

    c. π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘’π‘‘ π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  π‘₯ βˆ’ π‘Žπ‘₯𝑖𝑠

    d. π‘Ÿπ‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 360Β°

    4. Which transformation has occurred to quadrilateral BKHP?

    a. π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘’π‘‘ π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  𝑦 = π‘₯

    b. π‘Ÿπ‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 270Β° CCW

    c. π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘’π‘‘ π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  π‘₯ βˆ’ π‘Žπ‘₯𝑖𝑠

    d. π‘Ÿπ‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 360Β°

  • Find the coordinates of the vertices of each figure after the transformations.

    5. What would be the vertices of the image if the pre-image had vertices 𝐴(2, βˆ’2), 𝐡(1, 2), 𝐢(3,3), 𝐷(5, 2) and they were

    rotated 180Β° CW about the origin?

    a. 𝐴′(2, βˆ’2), 𝐡′(βˆ’1, 2), 𝐢′(βˆ’3,3), 𝐷′(βˆ’5, 2)

    b. 𝐴′(βˆ’2,2), 𝐡′(βˆ’1, βˆ’2), 𝐢′(βˆ’3, βˆ’3), 𝐷′(βˆ’5, βˆ’ 2)

    c. 𝐴′(βˆ’2, βˆ’2), 𝐡′(βˆ’1, βˆ’2), 𝐢′(βˆ’3, βˆ’3), 𝐷′(βˆ’5, 2)

    d. 𝐴′(2,2), 𝐡′(βˆ’1, βˆ’ 2), 𝐢′(βˆ’3,3), 𝐷′(βˆ’5, 2)

    6. What would be the vertices of the image if the pre-image had vertices 𝐴(2, βˆ’2), 𝐡(1, 2), 𝐢(3,3), 𝐷(5, 2) and they were

    reflected across the x-axis?

    a. 𝐴′(2, βˆ’2), 𝐡′(βˆ’1, 2), 𝐢′(βˆ’3,3), 𝐷′(βˆ’5, 2)

    b. 𝐴′(βˆ’2,2), 𝐡′(βˆ’1, βˆ’2), 𝐢′(βˆ’3, βˆ’3), 𝐷′(βˆ’5, βˆ’ 2)

    c. 𝐴′(βˆ’2, βˆ’2), 𝐡′(βˆ’1, βˆ’2), 𝐢′(βˆ’3, βˆ’3), 𝐷′(βˆ’5, 2)

    d. 𝐴′(2,2), 𝐡′(βˆ’1, 2), 𝐢′(3, βˆ’3), 𝐷′(5, βˆ’2)

    7. What would be the vertices of the image if the pre-image had vertices 𝐴(2, βˆ’2), 𝐡(1, 2), 𝐢(3,3), 𝐷(5, 2) and they were rotated 270Β° CCW about the origin?

    a. 𝐴′(2, βˆ’2), 𝐡′(βˆ’1, 2), 𝐢′(βˆ’3,3), 𝐷′(βˆ’5, 2)

    b. 𝐴′(βˆ’2,2), 𝐡′(βˆ’1, βˆ’2), 𝐢′(βˆ’3, βˆ’3), 𝐷′(βˆ’5, βˆ’ 2)

    c. 𝐴′(βˆ’2, βˆ’2), 𝐡′(2, βˆ’1), 𝐢′(3, βˆ’3), 𝐷′(2, βˆ’5)

    d. 𝐴′(2, βˆ’2), 𝐡′(2, 1), 𝐢′(3, βˆ’3), 𝐷′(2, 5)

    8. On the graph to the right draw and label the triangle with vertices 𝐴(βˆ’4, 5), 𝐡(3,2), 𝐢(βˆ’1,4) after all of the

    transformations listed below are done. DRAW all the images.

    1. π‘‡π‘Ÿπ‘Žπ‘›π‘ π‘™π‘Žπ‘‘π‘’π‘‘ 2 𝑒𝑛𝑖𝑑 π‘Ÿπ‘–π‘”β„Žπ‘‘ π‘Žπ‘›π‘‘ 2 𝑒𝑛𝑖𝑑𝑠 π‘‘π‘œπ‘€π‘›

    2. 𝑅𝑒𝑓𝑙𝑒𝑐𝑑 π‘Žπ‘π‘Ÿπ‘œπ‘ π‘  𝑦 = π‘₯

    3. π‘…π‘œπ‘‘π‘Žπ‘‘π‘’ 90 π‘‘π‘’π‘”π‘Ÿπ‘’π‘’π‘  πΆπΆπ‘Š π‘Žπ‘π‘œπ‘’π‘‘ π‘‘β„Žπ‘’ π‘œπ‘Ÿπ‘–π‘”π‘–π‘›

  • Vocabulary review: 9. List important Characteristics of each.

    a) Rigid Transformation/Isometry b) Translations

    c) Reflections d) Rotations e) Dilations f) Composition for Transformations

    10. What is the difference between two figures that are congruent and two figures that are similar?

    11. Name the ordered pair rule that transforms each figure into its image. Rule: (x, y) οƒ  ______________ Rule: (x, y) οƒ _____________ Rule: (x, y) οƒ _____________

  • Complete the following transformations on the figure:

    12. Reflect π‘‰π‘ˆπ‘Š across the y-axis, then translate it by the rule (π‘₯, 𝑦) β†’ (π‘₯ βˆ’ 3, 𝑦 + 4)

    13. Translate 𝐴𝐡𝐢𝐷 by the rule (π‘₯, 𝑦) β†’ (π‘₯ βˆ’ 5, 𝑦), then rotate the figure 180Β°.

    14.

  • Determine the scale factor for the dilations.

    15.

    a. π‘˜ = 2

    b. π‘˜ = 1

    c. π‘˜ = 1.5

    d. π‘˜ = 0

    16.

    a. π‘˜ = 2

    b. π‘˜ = 1

    c. π‘˜ = 0.5

    d. π‘˜ = 0

    17.

    a. π‘˜ = 2 .5

    b. π‘˜ = 0.25

    c. π‘˜ = 2

    d. π‘˜ = 0.50

    18.

    a. π‘˜ = 0.25

    b. π‘˜ = 2

    c. π‘˜ = 0.50

    d. π‘˜ = 2.5

  • Determine the coordinate points of the image after the pre-image provided is dilated by the scale factor listed.

    19. π‘˜ = 1

    2

    a. 𝐢’(2,0), π‘Œβ€™(0.5, 0.5), 𝐽’(1.5, 2.5)

    b. 𝐢’(1,0), π‘Œβ€™(2.5, 0.5), 𝐽’(1.5, 1.5)

    c. 𝐢’(1,0.5), π‘Œβ€™(2.5, 1.5), 𝐽’(2, 1.5)

    d. 𝐢’(1,1.5), π‘Œβ€™(2, 0.5), 𝐽’(0.5, 1.5)

    20. π‘˜ = 2

    a. 𝐷’(βˆ’2, 0), π‘Œβ€™(0, 4), 𝑍’(4, βˆ’2)

    b. 𝐷’(2, 0), π‘Œβ€™(2, βˆ’2), 𝑍’(1, βˆ’2)

    c. 𝐷’(βˆ’1, 0), π‘Œβ€™(0, 2), 𝑍’(2, βˆ’1)

    d. 𝐷’(βˆ’2, 2), π‘Œβ€™(2, 4), 𝑍’(0, βˆ’2)

    21. π‘˜ = 1

    4

    a. 𝐴’(0.25, 0.5), 𝐿’(2.25, 1.25), 𝑋’(1.75, 1.25)

    b. 𝐴’(1.5, 0.25), 𝐿’(1.75, 0.75), 𝑋’(1.75, 0.25)

    c. 𝐴’(0.25, 0.5), 𝐿’(1.25, 0.75), 𝑋’(1.25, 1.75)

    d. 𝐴’(0.5, 0.25), 𝐿’(1.25, 0.25), 𝑋’(1.25, 0.75)

    22. π‘˜ = 1.5

    a. 𝐽’(βˆ’0.5, βˆ’1.5), 𝑋’(0.5, 4.5), 𝐿’(2, 3), π‘Œβ€²(0, 4.5)

    b. 𝐽’(βˆ’1.5, βˆ’1.5), 𝑋’(1.5, 4.5), 𝐿’(3, 3), π‘Œβ€²(0, 4.5)

    c. 𝐽’(1.5, 1.5), 𝑋’(1.25, 4.5), 𝐿’(3, 3.5), π‘Œβ€²(0, βˆ’4.5)

    d. 𝐽’(βˆ’2.5, βˆ’1.25), 𝑋’(βˆ’1.5, 4), 𝐿’(3, βˆ’3), π‘Œβ€²(0, 4)

  • 23. Describe the sequences required for the following transformation below:

    24. Quadrilateral ABCD is rotated 90ο‚° counterclockwise (or 270 clockwise) about the origin. Name the new

    coordinates.

    Original Coordinates A (1, 3) B (3, 4) C (6, 5) D (1, 5)

    New Coordinates

    25. Find the Center of Dilation and the Scale Factor for the following:

    a)

  • b)

    26. Find the coordinates of the vertices of the figure after a dilation of k = 2 centered at the point (1, -3) and graph the image.

    X(______, _______) β†’ X’ (_____, ______)

    Y(______, _______) β†’ Y’ (_____, ______)

    Z(______, _______) β†’ Z’ (_____, ______)

    -14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14

    -8

    -7

    -6

    -5

    -4

    -3

    -2

    -1

    1

    2

    3

    4

    5

    6

    7

    8

    x

    y

    X

    Y

    Z

  • 27.

    28.

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