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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

NameDate

Circle the best answer.

  1. Luz dilates a quilt triangle with corners C(-3, 1), D(1, -3) and E(-1, 3) by scale factor 3/2 about corner C. Where is D′?

    • (6, -6)
    • (5/2, -3/2)
    • (3, -5)
    • (3/2, -9/2)

  2. Bo dilates segment AB, with A(1, 1) and B(5, 3), by scale factor 2 about A. Which statement about the image is right?

    • A′ = (2, 2) and B′ = (10, 6); the dilation is about the origin, not about A
    • A′ = A and B′ = (9, 5); the image lies on line AB and is twice as long
    • A′ = A and B′ = (9, 5); the image is parallel to AB, not on it
    • A′ = A and B′ = (7, 5); B moves 2 across and 2 up from where it began

  3. A dilation about the origin has scale factor 3/2. Kira dilates segment AB with A(2, 0), B(6, 4) and its midpoint M(4, 2). Is M′ the midpoint of A′B′?

    • Yes, because a dilation keeps the points where they are
    • Yes: A′(3, 0), B′(9, 6) and M′(6, 3), and the midpoint of A′B′ is (6, 3)
    • No, because a dilation stretches lengths, so a midpoint moves off center
    • No: M′ is (11/2, 7/2), while the midpoint of A′B′ is (6, 3)

  4. A dilation about the origin sends A(2, 5) to A′(6, 15). Ren wants B(4, -1). Where does B go?

    • (8, 9)
    • (4/3, -1/3)
    • (7, 2)
    • (12, -3)

  5. Esme dilates the line y = 3x − 2 by scale factor 2 about the origin. What is the image?

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

  6. Milo dilates the line y = 2x + 3 by scale factor 3 about C(1, 5). What is the image?

    • y = 6x + 3, because the slope doubles
    • y = 2x + 9, because the intercept triples
    • The same line, y = 2x + 3, because C(1, 5) is on it
    • y = 2x + 7, a parallel line, because lines move when dilated

  7. A dilation about the origin sends Pia's line y = 2x + 4 to the line y = 2x + 10. What is the scale factor?

    • 2/5
    • 6
    • 5/2
    • 14

  8. Tala's turtle triangle has area 12 cm². A dilation with scale factor 3/2 is applied. What is the image's area?

    • 27 cm²
    • 16/3 cm²
    • 27/2 cm²
    • 18 cm²

  9. Factor 3. Second dilation about the same C returns the original. Ari dilates a bike picture by 3 about C. A second dilation about C should bring the picture back to its original size. What is its scale factor?

    • 2/3
    • 9
    • 1/3
    • -3

  10. Esme dilates a triangle with corners P(4, 4), Q(8, 0) and R(8, 4) by scale factor 1/2 about corner P. Where is Q′, and is it closer to P or farther?

    • Q′ = (4, 0), closer to P than Q
    • Q′ = (6, 2), the same distance from P as Q
    • Q′ = (12, -4), farther from P than Q
    • Q′ = (6, 2), closer to P than Q
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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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