Worksheet

Similar shapes: a dilation plus moves

Grade 8 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

  1. Read this first

    Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The design and its copy are both drawn, with D, D′, F and F′ labeled; the middle step is not drawn.

  2. Luz's rocket design became a similar copy. D went from (2, 4) to (3, 3), and F from (4, -2) to (6, -6). Which moves did it, in order?

    • a slide 2 units down, then a dilation by 3/2 from the origin
    • a slide 2 units down, then a dilation by 2/3 from the origin
    • a dilation by 3/2 from the origin, then a slide 2 units down
    • a slide 1 unit right and 1 unit down

  3. Milo's boat design became a similar copy. D went from (2, 3) to (-3, 6), and F from (1, -2) to (-1, -4). Which moves did it, in order?

    • a dilation by 1/2 from the origin, then a flip across the y-axis, then a slide 1 unit right
    • a dilation by 2 from the origin, then a flip across the y-axis, then a slide 1 unit right
    • a slide 1 unit right, then a dilation by 2 from the origin, then a flip across the y-axis
    • a slide 5 units left and 3 units up

  4. Noah's car design became a similar copy. D went from (4, 2) to (-1, 3), and F from (-2, 4) to (-4, 4). Which moves did it, in order?

    • a slide 3 units left and 2 units up, then a dilation by 1/2 from the origin
    • a dilation by 1/2 from the origin, then a slide 3 units left and 2 units up
    • a slide 5 units left and 1 unit up
    • a dilation by 2 from the origin, then a slide 3 units left and 2 units up

  5. Ren slid a snowman sticker 2 units right and 2 units up, then dilated it by 3/2 from the origin. D′ is now at (-3, 6). Where did D start? Write it like (7, -3).

  6. Tala dilated a kite sticker by 1/2 from the origin, then slid it 2 units right and 4 units down. D′ is now at (4, -6). Where did D start? Write it like (7, -3).

  7. Zee dilated a butterfly sticker by 3 from the origin, then slid it 3 units right and 4 units down. D′ is now at (9, 5). Where did D start? Write it like (7, -3).

  8. Bo dilates a robot picture from the origin by 4, then dilates the copy by 1/2. One dilation from the origin would do both. What is its scale factor?

  9. Esme dilates a house picture from the origin by 1/2, then dilates the copy by 3. One dilation from the origin would do both. What is its scale factor?

  10. Jun dilates a kite picture by 2 from the origin, then turns it 90° counterclockwise. DF was 5 units and ∠D was 64°. What are D′F′ and ∠D′? Type: length, angle.

  11. Luz dilates a sled picture by 5/2 from the origin, then slides it 3 units right. DF was 4 units and ∠D was 35°. What are D′F′ and ∠D′? Type: length, angle.

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Similar shapes: a dilation plus moves

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

  1. Read this first

    Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The design and its copy are both drawn, with D, D′, F and F′ labeled; the middle step is not drawn.

  2. Luz's rocket design became a similar copy. D went from (2, 4) to (3, 3), and F from (4, -2) to (6, -6). Which moves did it, in order?

    • a slide 2 units down, then a dilation by 3/2 from the origin
    • a slide 2 units down, then a dilation by 2/3 from the origin
    • a dilation by 3/2 from the origin, then a slide 2 units down
    • a slide 1 unit right and 1 unit down

  3. Milo's boat design became a similar copy. D went from (2, 3) to (-3, 6), and F from (1, -2) to (-1, -4). Which moves did it, in order?

    • a dilation by 1/2 from the origin, then a flip across the y-axis, then a slide 1 unit right
    • a dilation by 2 from the origin, then a flip across the y-axis, then a slide 1 unit right
    • a slide 1 unit right, then a dilation by 2 from the origin, then a flip across the y-axis
    • a slide 5 units left and 3 units up

  4. Noah's car design became a similar copy. D went from (4, 2) to (-1, 3), and F from (-2, 4) to (-4, 4). Which moves did it, in order?

    • a slide 3 units left and 2 units up, then a dilation by 1/2 from the origin
    • a dilation by 1/2 from the origin, then a slide 3 units left and 2 units up
    • a slide 5 units left and 1 unit up
    • a dilation by 2 from the origin, then a slide 3 units left and 2 units up

  5. Ren slid a snowman sticker 2 units right and 2 units up, then dilated it by 3/2 from the origin. D′ is now at (-3, 6). Where did D start? Write it like (7, -3).

    (-4, 2)

  6. Tala dilated a kite sticker by 1/2 from the origin, then slid it 2 units right and 4 units down. D′ is now at (4, -6). Where did D start? Write it like (7, -3).

    (4, -4)

  7. Zee dilated a butterfly sticker by 3 from the origin, then slid it 3 units right and 4 units down. D′ is now at (9, 5). Where did D start? Write it like (7, -3).

    (2, 3)

  8. Bo dilates a robot picture from the origin by 4, then dilates the copy by 1/2. One dilation from the origin would do both. What is its scale factor?

    2

  9. Esme dilates a house picture from the origin by 1/2, then dilates the copy by 3. One dilation from the origin would do both. What is its scale factor?

    3/2

  10. Jun dilates a kite picture by 2 from the origin, then turns it 90° counterclockwise. DF was 5 units and ∠D was 64°. What are D′F′ and ∠D′? Type: length, angle.

    10, 64

  11. Luz dilates a sled picture by 5/2 from the origin, then slides it 3 units right. DF was 4 units and ∠D was 35°. What are D′F′ and ∠D′? Type: length, angle.

    10, 35