5.3 Transformations of the unit square in the x – y plane Quiz: AQA Further Maths, Unit 5

The 20 questions

1. Which matrix represents reflection in the x-axis (y = 0)?

   • [[1, 0], [0, -1]]
   • [[-1, 0], [0, 1]]
   • [[0, -1], [1, 0]]
   • [[0, 1], [1, 0]]

2. Which matrix represents reflection in the y-axis (x = 0)?

   • [[0, 1], [1, 0]]
   • [[-1, 0], [0, -1]]
   • [[1, 0], [0, -1]]
   • [[-1, 0], [0, 1]]

3. Which matrix represents reflection in the line y = x?

   • [[0, 1], [1, 0]]
   • [[0, -1], [-1, 0]]
   • [[1, 0], [0, -1]]
   • [[-1, 0], [0, -1]]

4. Which matrix represents a 90 degree anticlockwise rotation about the origin?

   • [[0, 1], [-1, 0]]
   • [[0, -1], [1, 0]]
   • [[1, 1], [0, 1]]
   • [[1, 0], [0, -1]]

5. Which matrix represents a 180 degree rotation about the origin?

   • [[1, 0], [0, 1]]
   • [[0, 1], [1, 0]]
   • [[0, -1], [1, 0]]
   • [[-1, 0], [0, -1]]

6. Which matrix represents an enlargement of scale factor 3 centred on the origin?

   • [[1, 3], [0, 1]]
   • [[3, 0], [0, 3]]
   • [[3, 0], [0, 1]]
   • [[0, 3], [3, 0]]

7. Under the matrix [[2, 0], [0, 1]], the area of the unit square becomes what?

   • 0.5
   • 4
   • 1
   • 2

8. Under a 90 degree anticlockwise rotation [[0, -1], [1, 0]], the point (1, 0) maps to what?

   • (0, 1)
   • (1, 1)
   • (0, -1)
   • (-1, 0)

9. Under reflection in y = -x, with matrix [[0, -1], [-1, 0]], what is the image of (1, 1)?

   • (1, -1)
   • (-1, 1)
   • (-1, -1)
   • (1, 1)

10. Under [[1, 0], [0, -1]], the point (2, 3) maps to what?

    • (-2, -3)
    • (2, -3)
    • (-2, 3)
    • (3, 2)

11. Under the reflection in x = 0 with matrix [[-1, 0], [0, 1]], what is the image of (4, -5)?

    • (4, 5)
    • (-4, -5)
    • (5, 4)
    • (-4, 5)

12. The unit square is enlarged by factor 2 centred on the origin. What is the image of corner (1, 1)?

    • (3, 3)
    • (2, 1)
    • (1, 2)
    • (2, 2)

13. Matrix [[0, 1], [-1, 0]] represents which rotation about the origin?

    • 270 degrees clockwise
    • 90 degrees clockwise
    • 90 degrees anticlockwise
    • 180 degrees

14. What is the area of the image of the unit square under [[0, -1], [1, 0]]?

    • 1
    • 0
    • 2
    • 4

15. Where must enlargements be centred for 2 × 2 matrix transformations in this specification?

    • The origin
    • Point (1, 0)
    • Any point
    • Point (1, 1)

16. Under [[2, 0], [0, 3]], what is the area of the image of the unit square?

    • 5
    • 12
    • 6
    • 3

17. Under a 270 degree anticlockwise rotation [[0, 1], [-1, 0]], what is the image of (1, 0)?

    • (1, 0)
    • (0, 1)
    • (0, -1)
    • (-1, 0)

18. Point (2, 5) is reflected in x = 0 and then in y = 0. What is the final image?

    • (2, -5)
    • (-2, -5)
    • (5, 2)
    • (-2, 5)

19. What transformation about the origin is represented by the matrix with rows [-1, 0] and [0, -1]?

    • 180° rotation
    • Reflection in y-axis
    • 90° clockwise rotation
    • Reflection in x-axis

20. Under the enlargement with factor -2 centred on the origin, the point (1, 3) maps to what?

    • (2, 6)
    • (-2, -6)
    • (-2, 6)
    • (-1, -3)

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