Worksheet

What a dilation does to length, perimeter and area

Grade 8 Math Worksheet - Challenge Me

NameDate

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

  1. Kira's quilt design covers 12 square units. After a dilation from the origin, the image covers 27 square units. What is the scale factor from old to new?

  2. Luz's window design covers 32 square units. After a dilation from the origin, the image covers 2 square units. What is the scale factor from old to new?

  3. Milo's table design covers 25 square units. After a dilation from the origin, the image covers 4 square units. What is the scale factor from old to new?

  4. Pia dilates a quilt design from the origin by 5/4. How do the perimeter and the area of the image compare with the original?

    • The perimeter and the area are both 5/4 times as much.
    • The perimeter and the area are both 25/16 times as much, since both use that factor.
    • The perimeter is 5/4 times as long, and the area is 5/2 times as much.
    • The perimeter is 5/4 times as long, and the area is 25/16 times as much.

  5. Ren dilates a book design from the origin by 4. How do the perimeter and the area of the image compare with the original?

    • The perimeter is 4 times as long, and the area is 16 times as much.
    • The perimeter is 4 times as long, and the area is 8 times as much.
    • The perimeter and the area are both 4 times as much, since both grow alike.
    • The perimeter and the area are both 16 times as much.

  6. Tala dilates a window design from the origin by 1/4. How do the perimeter and the area of the image compare with the original?

    • The perimeter is 1/4 times as long, and the area is 1/16 times as much.
    • The perimeter and the area are both 1/4 times as much.
    • The perimeter and the area are both 1/16 times as much.
    • The perimeter is 1/4 times as long, and the area is 1/2 times as much.

  7. After a dilation from the origin by 2/3, the image of Ari's quilt design covers 12 square units. How many square units did the original cover?

  8. After a dilation from the origin by 5/4, the image of Bo's table design covers 50 square units. How many square units did the original cover?

  9. 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 window rectangle with corners (-6, -6) and (6, 3) marked; the image is not drawn.

  10. Jun's window is a rectangle with opposite corners (-6, -6) and (6, 3), dilated from the origin by 2/3. What are the image's perimeter and area? Type: perimeter, area.

  11. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle. The rug rectangle with corners (-3, 3) and (6, 6) marked; the image is not drawn.

  12. Kira's rug is a rectangle with opposite corners (-3, 3) and (6, 6), dilated from the origin by 4/3. What are the image's perimeter and area? Type: perimeter, area.

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What a dilation does to length, perimeter and area

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

  1. Kira's quilt design covers 12 square units. After a dilation from the origin, the image covers 27 square units. What is the scale factor from old to new?

    3/2

  2. Luz's window design covers 32 square units. After a dilation from the origin, the image covers 2 square units. What is the scale factor from old to new?

    1/4

  3. Milo's table design covers 25 square units. After a dilation from the origin, the image covers 4 square units. What is the scale factor from old to new?

    2/5

  4. Pia dilates a quilt design from the origin by 5/4. How do the perimeter and the area of the image compare with the original?

    • The perimeter and the area are both 5/4 times as much.
    • The perimeter and the area are both 25/16 times as much, since both use that factor.
    • The perimeter is 5/4 times as long, and the area is 5/2 times as much.
    • The perimeter is 5/4 times as long, and the area is 25/16 times as much.

  5. Ren dilates a book design from the origin by 4. How do the perimeter and the area of the image compare with the original?

    • The perimeter is 4 times as long, and the area is 16 times as much.
    • The perimeter is 4 times as long, and the area is 8 times as much.
    • The perimeter and the area are both 4 times as much, since both grow alike.
    • The perimeter and the area are both 16 times as much.

  6. Tala dilates a window design from the origin by 1/4. How do the perimeter and the area of the image compare with the original?

    • The perimeter is 1/4 times as long, and the area is 1/16 times as much.
    • The perimeter and the area are both 1/4 times as much.
    • The perimeter and the area are both 1/16 times as much.
    • The perimeter is 1/4 times as long, and the area is 1/2 times as much.

  7. After a dilation from the origin by 2/3, the image of Ari's quilt design covers 12 square units. How many square units did the original cover?

    27

  8. After a dilation from the origin by 5/4, the image of Bo's table design covers 50 square units. How many square units did the original cover?

    32

  9. 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 window rectangle with corners (-6, -6) and (6, 3) marked; the image is not drawn.

  10. Jun's window is a rectangle with opposite corners (-6, -6) and (6, 3), dilated from the origin by 2/3. What are the image's perimeter and area? Type: perimeter, area.

    28, 48

  11. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle. The rug rectangle with corners (-3, 3) and (6, 6) marked; the image is not drawn.

  12. Kira's rug is a rectangle with opposite corners (-3, 3) and (6, 6), dilated from the origin by 4/3. What are the image's perimeter and area? Type: perimeter, area.

    32, 48