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. Jun's rug design covers 18 square units. After a dilation from the origin, the image covers 8 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. Noah dilates a rug design from the origin by 3/2. How do the perimeter and the area of the image compare with the original?

    • The perimeter and the area are both 9/4 times as much.
    • The perimeter and the area are both 3/2 times as much, since both grow alike.
    • The perimeter is 3/2 times as long, and the area is 9/4 times as much.
    • The perimeter is 3/2 times as long, and the area is 3 times as much.

  5. 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 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.
    • 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.

  6. After a dilation from the origin by 3/2, the image of Zee's rug design covers 45 square units. How many square units did the original cover?

  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. Esme's door is a rectangle with opposite corners (-4, 2) and (4, 6), dilated from the origin by 3/2. What are the image's perimeter and area? Type: perimeter, area.

  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. Jun's rug design covers 18 square units. After a dilation from the origin, the image covers 8 square units. What is the scale factor from old to new?

    2/3

  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. Noah dilates a rug design from the origin by 3/2. How do the perimeter and the area of the image compare with the original?

    • The perimeter and the area are both 9/4 times as much.
    • The perimeter and the area are both 3/2 times as much, since both grow alike.
    • The perimeter is 3/2 times as long, and the area is 9/4 times as much.
    • The perimeter is 3/2 times as long, and the area is 3 times as much.

  5. 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 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.
    • 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.

  6. After a dilation from the origin by 3/2, the image of Zee's rug design covers 45 square units. How many square units did the original cover?

    20

  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. Esme's door is a rectangle with opposite corners (-4, 2) and (4, 6), dilated from the origin by 3/2. What are the image's perimeter and area? Type: perimeter, area.

    36, 72

  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