Transformation matrices

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Pia turns a rocket design 90° clockwise about the origin with V = [1, 4, 2; 3, -2, 5], columns C, D and F. Where is D′, written like (8, -1)?

   (-2, -4)
2. 2.

   Ren enlarges a star design by scale factor 3 about the origin with V = [1, -2, 3; 2, 1, -1], columns C, D and F. Where is F′, written like (8, -1)?

   (9, -3)
3. 3.

   Zee turns a robot design 90° counterclockwise about the origin with V = [2, -1, 6; 5, 3, 1], columns C, D and F. Where is D′, written like (8, -1)?

   (-3, -1)
4. 4.

   Esme reflects a kite design over the line y = x with V = [6, 1, -3; 2, -5, 4], columns C, D and F. Where is F′, written like (8, -1)?

   (4, -3)
5. 5.

   Jun multiplies a robot design's vertex matrix by [0, 1; -1, 0]. What does this matrix do?

   • Turns 180° about the origin
   • Reflects over the line through (0, 0) and (1, 1)
   • Turns 90° counterclockwise about the origin
   • Turns 90° clockwise about the origin
6. 6.

   Kira multiplies a star design's vertex matrix by [3, 0; 0, 3]. What does this matrix do?

   • Turns 180° about the origin
   • Enlarges by scale factor 3 about the origin
   • Slides every point 3 right and 3 up on the grid
7. 7.

   Luz multiplies a boat design's vertex matrix by [0, -1; 1, 0]. What does this matrix do?

   • Turns 180° about the origin
   • Reflects over the line through (0, 0) and (1, 1)
   • Turns 90° counterclockwise about the origin
   • Turns 90° clockwise about the origin
8. 8.

   Milo multiplies a quilt block's vertex matrix by [2, 0; 0, 2]. What does this matrix do?

   • Enlarges by scale factor 2 about the origin
   • Turns 180° about the origin
   • Slides every point 2 right and 2 up
9. 9.

   Pia applies a reflection over the x-axis to a pencil line with vertex matrix V = [-3, 4; 2, 6], columns C and D. Which matrix is the image?

   • [-3, 4; -2, -6]
   • [-3, -4; 2, -6]
   • [3, -4; 2, 6]
   • [3, -4; -2, -6]
10. 10.

    Ren applies a 90° counterclockwise turn about the origin to a kite string drawing with vertex matrix V = [1, 4; 3, -2], columns C and D. Which matrix is the image?

    • [4, -1; -2, -3]
    • [-3, 2; 1, 4]
    • [3, -2; -1, -4]
    • [-1, -4; -3, 2]