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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 - Challenge Me

NameDate

Circle the best answer.

  1. Luz's dilation has center P(1, -2). It sends D(4, 2) to D′(13, 14). What is the scale factor?

    • 1/4
    • 3
    • 20
    • 4

  2. Zee's leaf triangle is dilated by scale factor 5/2. How do the image's perimeter and area compare with the original's?

    • Both unchanged, since the shape is the same
    • Perimeter 25/4 times as large; area 5/2 times as large
    • Perimeter 5/2 times as large; area 5/2 times as large
    • Perimeter 5/2 times as large; area 25/4 times as large

  3. Bo's circle has center (2, -1) and radius 3. A dilation about the origin with scale factor 2 is applied. What is the image circle?

    • Center (4, -2), radius 3
    • Center (4, -2), radius 6
    • Center (2, -1), radius 6
    • Center (4, -2), radius 5

  4. Tala dilates segment AB with A(6, 3) and B(6, -5) by scale factor 1/2 about P(-2, 3), which is not on AB. Where are A′ and B′?

    • A′(13/2, 7/2) and B′(13/2, -9/2)
    • A′(3, 3/2) and B′(3, -5/2)
    • A′(4, 0) and B′(4, -4)
    • A′(2, 3) and B′(2, -1)

  5. Milo dilates by 2 about the origin, then by 1/2 about P(4, 0). Which single transformation does the pair equal?

    • A translation 2 units right
    • A translation 4 units right
    • The identity, since 2 × 1/2 = 1 and nothing moves
    • A translation 2 units left

  6. The center is not given. A dilation with scale factor 3 sends Pia's boat point A(2, 1) to A′(6, 3). Where does B(4, 5) go?

    • (8, 7)
    • (12, 15)
    • (12, 5)
    • (7, 8)

  7. Ren claims A is always the midpoint of PA′. With P(1, 1) and A(4, 3), Ren tests scale factor 3. What does the test show?

    • True: it works when the factor is 2, so it works for any other factor too, such as 3
    • False: with factor 3, A′ = (7, 6) and the midpoint of PA′ is (4, 3.5), not A
    • False: with factor 3, A′ = (10, 7) and the midpoint of PA′ is (5.5, 4), not A
    • True: A′ lies on line PA, so A is a midpoint

  8. Perimeter 14 cm, area 8 cm². Scale factor 1/3. A dilation with scale factor 1/3 makes Jun's star triangle have perimeter 14 cm and area 8 cm². What were the original perimeter and area?

    • Perimeter 14/3 cm, area 8/9 cm²
    • Perimeter 42 cm, area 72 cm²
    • Perimeter 42 cm, area 24 cm²
    • Perimeter 17 cm, area 11 cm²

  9. A dilation with scale factor 3 about C(1, 0) sends line m to y = 2x + 7. Esme works back. What was m?

    • y = 2x + 21
    • y = 2x + 1
    • y = 2x + 7/3
    • y = 2x + 4

  10. Ari's projector lamp is the center. A 3 cm wide slide is 20 cm from the lamp, and the screen is 100 cm from it. How wide is the image?

    • 0.6 cm, using scale factor 1/5
    • 240 cm, using scale factor 80
    • 5 cm, the scale factor itself
    • 15 cm, using scale factor 5
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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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