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

   Esme wants to slide a design 8 units right using two flips across vertical lines. The first line is x = 1. Where must the second line be?

   • x = 5
   • x = 9
   • x = 4
   • x = -3
3. 3.

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

   • A 90° counterclockwise turn about the origin
   • A flip across the y-axis
   • A 90° clockwise turn about the origin
   • A 45° counterclockwise turn about the origin
4. 4.

   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
5. 5.

   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 50° clockwise turn about O
   • A flip across a line through O
   • A 25° counterclockwise turn about O
   • A 50° counterclockwise turn about O
6. 6.

   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
7. 7.

   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
8. 8.

   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
9. 9.

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

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

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. 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?

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