Sequences of transformations, including glide reflections

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

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

   • A flip across the line x = 0.5
   • A slide 5 units right
   • A slide 10 units left
   • A slide 10 units right
2. 2.

   Jun flips a design across x = 2, then across y = 3. Which single move gives the same result?

   • A 180° turn about the point (2, 3)
   • A 90° turn about the point (2, 3)
   • A slide 4 units right and 6 units up
   • A 180° turn about the origin
3. 3.

   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?

   2
4. 4.

   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?

   -5
5. 5.

   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
6. 6.

   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?

   -6

7. Read this first

   Use this

   A design whose corners go around clockwise. The pattern uses exactly 2 flips, 1 turn and 3 slides, in any order.

8. 7.

   Noah builds a pattern with 2 flips, 1 turn and 3 slides in some order. Could the final image be a mirror image of the start?

   • Yes: 2 flips and a turn together make a mirror image
   • Yes: the 3 slides can leave the corners going the other way
   • No: two flips reverse the corner order twice, and turns and slides never reverse it
   • Yes: a flip always makes a mirror image, whatever comes after it
9. 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 180° turn about the point (2, 1)
   • A slide 4 units right
   • A flip across the line y = 1
10. 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 left and 2 down, then flip across the x-axis
    • Flip across the y-axis, then slide 3 left and 2 down
    • Slide 3 left and 2 down, then flip across the y-axis
    • Slide 3 right and 2 up, then flip across the y-axis

11. 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).

12. 10.

    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 left, then turn 90° counterclockwise about the origin
    • Turn 90° counterclockwise about the origin, then slide 4 left
    • Turn 90° counterclockwise about the origin, then slide 4 right
    • Slide 4 right, then turn 90° clockwise about the origin