Math 9 · Unit 13: Position and transformation · Cambridge Lower Secondary Maths Stage 9

Questions

1. 1. Triangle A is reflected in the mirror line x = 3. Triangle B is the image. Which are the corners of B?

   • (1, 2), (2, 1), (2, 3)
   • (5, 4), (4, 5), (4, 3)
   • (4, 4), (3, 5), (3, 3)
   • (6, 4), (5, 5), (5, 3)
   Check

2. 2. Triangle B has corners (5, 4), (4, 5) and (4, 3). It is translated by the column vector (2 over −1). Triangle C is the image. Which are the corners of C?

   • (6, 2), (5, 3), (5, 1)
   • (3, 5), (2, 6), (2, 4)
   • (7, 3), (6, 4), (6, 2)
   • (7, 5), (6, 6), (6, 4)
   Check

3. 3. Rectangle A is rotated 90° clockwise about the centre (3, 4), marked ×. Rectangle B is the image. Which are the corners of B?

   • (3, 4), (5, 4), (5, 5), (3, 5)
   • (3, 4), (4, 4), (4, 6), (3, 6)
   • (3, 4), (2, 4), (2, 2), (3, 2)
   • (3, 4), (3, 3), (5, 3), (5, 4)
   Check

4. 4. Rectangle B has corners (3, 4), (4, 4), (4, 6) and (3, 6). It is reflected in the mirror line y = 3. Rectangle C is the image. Which are the corners of C?

   • (3, 2), (4, 2), (4, 4), (3, 4)
   • (3, 1), (4, 1), (4, 3), (3, 3)
   • (3, 3), (4, 3), (4, 5), (3, 5)
   • (3, 0), (4, 0), (4, 2), (3, 2)
   Check

5. 5. The diagram shows shape A. Cards a, b and c show three combinations of transformations. Diagrams i, ii and iii show shape A and its image, shape B. Match each card with the correct diagram.

   • a: reflection in the line x = 3, then translation (1 over −1)
   • b: rotation of 180°, centre (3, 3), then translation (−2 over −1)
   • c: rotation of 90° clockwise, centre (1, 3), then reflection in the line y = 2

   • iii
   • i
   • ii
   Check

6. 6. Triangle A is reflected to give triangle B. What is the equation of the mirror line?

   • x = 2
   • x = 3
   • x = 4
   • y = 3
   Check

7. 7. Triangle A is translated to give triangle C. What is the column vector?

   • (6 over −2)
   • (2 over 6)
   • (7 over 4)
   • (6 over 2)
   Check

8. 8. Triangle A is rotated anticlockwise to give triangle D. What are the angle and the centre of the rotation?

   • 90°, centre (1, 2)
   • 180°, centre (1, 4)
   • 90°, centre (1, 4)
   • 90°, centre (3, 4)
   Check

9. 9. Triangle B is reflected to give triangle E. What is the equation of the mirror line?

   • y = 6
   • x = 5
   • y = 5
   • y = 4
   Check

10. 10. Triangle E is rotated to give triangle C. What are the angle and the centre of the rotation?

    • 180°, centre (6, 6)
    • 90°, centre (6, 6)
    • 180°, centre (6, 5)
    • 180°, centre (5, 6)
    Check

11. 11. Triangle C is translated to give triangle F. What is the column vector?

    • (−3 over −1)
    • (−1 over 3)
    • (−1 over −3)
    • (1 over 3)
    Check

12. 12. Triangle A is translated by the column vector (−4 over 1), then reflected in the line y = 4. Triangle B is the image. Which are the corners of B?

    • (1, 1), (3, 1), (2, 3)
    • (1, 7), (3, 7), (2, 5)
    • (1, 3), (3, 3), (2, 5)
    • (1, −1), (3, −1), (2, 1)
    Check

13. 13. Triangle A is rotated 90° anticlockwise about (5, 4), then translated by the column vector (0 over −3). Triangle C is the image. Which are the corners of C?

    • (3, 4), (3, 6), (5, 5)
    • (0, 4), (0, 6), (2, 5)
    • (7, 1), (7, −1), (5, 0)
    • (3, 1), (3, 3), (5, 2)
    Check

14. 14. Triangle A is reflected in the line x = 5, then rotated 180° about (5, 3). Triangle D is the image. Which are the corners of D?

    • (8, 3), (8, 5), (6, 4)
    • (5, 0), (7, 0), (6, 2)
    • (5, 0), (3, 0), (4, 2)
    • (5, 6), (3, 6), (4, 4)
    Check

15. 15. Triangle A is reflected in the y-axis, then translated by the column vector (2 over 1). Which are the corners of the image?

    • (2, −3), (1, −1), (−1, −3)
    • (4, −4), (3, −2), (1, −4)
    • (−2, 5), (−1, 3), (1, 5)
    • (6, −3), (3, −3), (5, −1)
    Check

16. 16. Triangle A is rotated 180° about (−2, −2), then reflected in the x-axis. Which are the corners of the image?

    • (0, 0), (−3, 0), (−1, 2)
    • (4, −4), (3, −2), (1, −4)
    • (0, 0), (1, −2), (3, 0)
    • (0, 0), (−1, −2), (−3, 0)
    Check

17. 17. Triangle A is translated by the column vector (−2 over 6), then rotated 90° anticlockwise about (−3, 5). Which are the corners of the image?

    • (−6, 8), (−4, 7), (−6, 5)
    • (0, 2), (0, 5), (−2, 3)
    • (0, 8), (−1, 6), (−3, 8)
    • (−6, 2), (−5, 4), (−3, 2)
    Check

18. 18. Triangle A is translated by the column vector (6 over 7), then reflected in the line x = 4. Which are the corners of the image?

    • (6, 3), (3, 3), (5, 5)
    • (4, 3), (3, 5), (1, 3)
    • (2, 3), (3, 5), (5, 3)
    • (2, 5), (3, 3), (5, 5)
    Check

19. 19. This is part of Rhian's homework. Is Rhian's homework correct?

    • Yes
    • No
    Check

20. 20. Which transformation takes shape N to shape I?

    • translation (6 over 4)
    • translation (4 over 6)
    • reflection in the line y = −1
    • translation (−4 over −6)
    Check