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10th grade Dilations from any center, and what a dilation does to lines worksheet

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Dilations from any center, and what a dilation does to lines

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Ren dilates a rocket sticker by scale factor 3 about its corner C(2, -1). Another corner D is at (5, 3). Where is D′?

    • (8, 6)
    • (15, 9)
    • (9, 12)
    • (11, 11)

  2. Luz's boat sticker was dilated by scale factor 3 about its corner C(1, 3). The image corner D′ is at (7, 9). Where was D?

    • (4, 6)
    • (19, 21)
    • (2, 2)
    • (3, 5)

  3. Side AB = 7 cm. Scale factor 3/2. Side AB of Pia's tent flap is 7 cm long. A dilation with scale factor 3/2 is applied. How long is A′B′?

    • 14/3 cm
    • 17/2 cm
    • 7 cm
    • 21/2 cm

  4. Image side A′B′ = 18 cm. Scale factor 3. A dilation with scale factor 3 makes side A′B′ of Bo's bus picture 18 cm long. How long was AB?

    • 6 cm
    • 15 cm
    • 18 cm
    • 54 cm

  5. Noah's quilt patch is a square with side 4 cm. A dilation with scale factor 3 is applied. What is the area of the image?

    • 12 cm²
    • 19 cm²
    • 48 cm²
    • 144 cm²

  6. Tala's star triangle has angles 40°, 60° and 80°. A dilation with scale factor 2 is applied. What are the image's angles?

    • 42°, 62° and 82°, each plus 2
    • 80°, 120° and 160°, each doubled
    • 20°, 30° and 40°, each halved
    • 40°, 60° and 80°, unchanged

  7. Ari's dilation about the origin has scale factor 3. It sends D(1, 2) to D′(3, 6) and F(2, 1) to F′(6, 3). How does line D′F′ compare with line DF?

    • A different line, parallel to DF, because DF misses the center
    • A line with slope -3, because the dilation multiplies slopes by 3
    • A line that crosses DF at the origin
    • The same line, because the slope is the same

  8. Line ℓ is y = 2x. It passes through Esme's center, the origin. The dilation has scale factor 3. What is the image of ℓ?

    • The same line, y = 2x
    • y = 2x + 3
    • y = 6x
    • y = 2x + 6, a parallel line, since dilations move lines

  9. Line m is y = 2x + 1. Jun dilates m by scale factor 3 about the origin. What is the image of m?

    • y = 2x + 4
    • y = 2x + 1
    • y = 6x + 3
    • y = 2x + 3

  10. A dilation about corner C sends Zee's corner D to D′. Using the coordinates on the card, what is the scale factor?

    • 4
    • 3
    • 1/3
    • 2
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10th grade Dilations from any center, and what a dilation does to lines worksheet – printable
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About this worksheet

Dilations from any center. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can dilate a point by a scale factor about any center, not only the origin.
  • I can say what happens to a line: through the center it stays, otherwise it moves parallel.
  • I can find a length before or after, the scale factor, and the center of a dilation.

Standard: G-SRT.A.1

Words to know

dilation: Every point moves along the line from the center, its distance multiplied by k.

center of dilation: The one point that does not move.

scale factor k: The number every distance from the center, and every length, is multiplied by.

enlargement, reduction: k more than 1 makes it bigger; k between 0 and 1 makes it smaller.

parallel lines: Lines with the same slope that never meet.

Common mistakes

Added or subtracted the scale factor instead of multiplying by it.

Multiplied the distance from the center but did not add the center back.

Dilated about the origin instead of the center named.

What to say

Ask: if a photo is enlarged 3 times, is a 2 cm side 5 cm or 6 cm?

Ask: which point stays still in this dilation?

Ask: which point stays still in this dilation?

Questions parents ask

What is the most common mistake with dilations from any center, and what a dilation does to lines?

Added or subtracted the scale factor instead of multiplying by it.

How can I help my child with dilations from any center, and what a dilation does to lines?

Ask: if a photo is enlarged 3 times, is a 2 cm side 5 cm or 6 cm?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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