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Grade 10 · Math · Geometry

10th grade Sequences of transformations, including glide reflections worksheet

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Sequences of transformations, including glide reflections

Grade 10 Math Worksheet - Challenge Me

NameDate

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

  1. Luz flips a design across x = -2, then across x = 3. Which single move gives the same result?

    • A slide 5 units right
    • A slide 10 units left
    • A flip across the line x = 0.5
    • A slide 10 units right

  2. Bo flips a design across the x-axis, then across the line y = x. Which single move gives the same result?

    • A 90° clockwise turn about the origin
    • A flip across the y-axis
    • A 90° counterclockwise turn about the origin
    • A 45° counterclockwise turn about the origin

  3. Ren's two mirror lines cross at O, and the second is 25° counterclockwise from the first. A design is flipped across the first, then the second. Which single move is that?

    • A 25° counterclockwise turn about O
    • A 50° counterclockwise turn about O
    • A 50° clockwise turn about O
    • A flip across a line through O

  4. Tala flips a design across x = 4, then across x = k. A flag pole starts at x = 1 and ends at x = -3. What is k?

  5. Zee flips a design across y = 2, then across y = k. A window top starts at y = 6 and ends at y = -8. What is k?

  6. Ari flips a design across x = 1, then across x = k. A kite tip starts at x = -3 and ends at x = 9. What is k?

  7. Pia flips a design across y = -1, then across y = k. A roof corner starts at y = 2 and ends at y = -8. What is k?

  8. Kira flips a tile across x = 0, then x = 2, then y = 1. Which single move gives the same result?

    • A slide 4 units right, then a flip across y = 1
    • A slide 4 units right
    • A flip across the line y = 1
    • A 180° turn about the point (2, 1)

  9. The new sequence must take the final image back to (x, y). Milo flips a design across the y-axis, then slides it 3 right and 2 up. Which sequence puts it exactly back where it started?

    • Slide 3 right and 2 up, then flip across the y-axis
    • Flip across the y-axis, then slide 3 left and 2 down
    • Slide 3 left and 2 down, then flip across the x-axis
    • Slide 3 left and 2 down, then flip across the y-axis

  10. Read this first

    Use this

    A design with corner (x, y). Move 1: a slide 4 units right. Move 2: a 90° clockwise turn about the origin. The new sequence must take the final image back to (x, y).

  11. Luz slides a design 4 units right, then turns it 90° clockwise about the origin. Which sequence puts it exactly back where it started?

    • Slide 4 right, then turn 90° clockwise about the origin
    • Slide 4 left, then turn 90° counterclockwise about the origin
    • Turn 90° counterclockwise about the origin, then slide 4 right
    • Turn 90° counterclockwise about the origin, then slide 4 left
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10th grade Sequences of transformations, including glide reflections worksheet – printable
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About this worksheet

Sequences of transformations. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can say what two moves in a row do, and find a missing slide or mirror line from a corner and its image.
  • I can say that two flips make a slide (parallel lines) or a turn (crossing lines), and how big.
  • I can test one point to tell whether the order of two moves matters, and undo a sequence in reverse order.

Standard: G-CO.A.5, G-CO.A.2

Words to know

sequence of moves: Moves done one after another, each starting where the last one ended.

composition: The math word for one move followed by another.

glide reflection: A slide along a mirror line, then a flip across that line.

undo a move: The move back: slide back, flip again, or turn the other way.

image: The shape after the moves; D becomes D′.

rigid motion: A slide, flip or turn: lengths and angles stay the same.

mirror line: The line a flip is across; it sits halfway between a point and its image.

orientation: The order the corners run round, clockwise or counterclockwise; a flip reverses it.

Common mistakes

Your child solved for x and stopped.

Your child set the two expressions equal but moved a number across with the wrong sign. Check each step by putting x back in.

Your child found how far the image is from the start and forgot that a flip or turn came first.

What to say

Ask: what does the question want to know, x or the length or angle?

Ask: where is the shape after move 1?

Questions parents ask

What is the most common mistake with sequences of transformations, including glide reflections?

Your child solved for x and stopped.

How can I help my child with sequences of transformations, including glide reflections?

Ask: what does the question want to know, x or the length or angle?

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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