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

Questions

1. 1. Enlarge the triangle with scale factor 4 from the centre of enlargement, the ×. Which description gives the corners of the enlarged triangle?

   • the ×, 6 squares right and 3 up of the ×, and 6 squares right of the ×
   • the ×, 8 squares right and 4 up of the ×, and 8 squares right of the ×
   • the ×, 4 squares right and 2 up of the ×, and 4 squares right of the ×
   • the ×, 8 squares right and 1 up of the ×, and 8 squares right of the ×
   Check

2. 2. This is part of Kurt's homework: enlarge the kite with scale factor 3 from the dot. Which mistake has Kurt made?

   • The top point should be 3 squares above the dot, not 2.
   • He has used scale factor 2 instead of 3.
   • The bottom point should be 6 squares below the dot, not 9.
   • The side points should be 9 squares from the dot, not 6.
   Check

3. 3. Shape A is enlarged with scale factor 3 and centre (6, 4). What are the corners of the image, C?

   • (−2, 0), (−2, 8), (2, 8), (6, 4), (6, 0)
   • (2, 2), (2, 6), (4, 6), (6, 4), (6, 2)
   • (12, 9), (12, 15), (15, 15), (18, 12), (18, 9)
   • (0, 1), (0, 7), (3, 7), (6, 4), (6, 1)
   Check

4. 4. A trapezium has vertices (2, 2), (3, 2), (5, 4) and (2, 4). It is enlarged by scale factor 2 with centre (3, 3). What are the image's vertices?

   • (5, 5), (3, 5), (7, 1), (5, 1)
   • (1, 1), (3, 1), (7, 5), (2, 5)
   • (1, 1), (3, 1), (7, 5), (1, 5)
   • (4, 4), (6, 4), (10, 8), (4, 8)
   Check

5. 5. Square M has perimeter 12 cm and area 9 cm². It is enlarged by a scale factor of 4 to become square N. Complete the working to find the perimeter and area of square N.

   Fill the blanks with these.

   • 48
   • 36
   • 192
   • 144
   Check

6. 6. Trapezium W has perimeter 18 cm and area 18 cm². It is enlarged by scale factor 2. What are the perimeter and area of the image?

   • perimeter 20 cm, area 20 cm²
   • perimeter 36 cm, area 36 cm²
   • perimeter 72 cm, area 36 cm²
   • perimeter 36 cm, area 72 cm²
   Check

7. 7. Triangle B is an enlargement of triangle A. Describe the enlargement.

   • enlargement, scale factor 3, centre (6, 2)
   • enlargement, scale factor 3, centre (2, 6)
   • enlargement, scale factor 2, centre (6, 2)
   • enlargement, scale factor 3, centre (0, 0)
   Check

8. 8. Triangle C is an enlargement of triangle A. Describe the enlargement.

   • enlargement, scale factor 3, centre (3, 5)
   • enlargement, scale factor 2, centre (3, 5)
   • enlargement, scale factor 2, centre (1, −1)
   • enlargement, scale factor 2, centre (5, 3)
   Check

9. 9. The vertices of rectangle P are at (0, −2), (−6, −2), (−6, 1) and (0, 1). The vertices of rectangle Q are at (4, 0), (2, 0), (2, 1) and (4, 1). Rectangle P is an enlargement of rectangle Q. Describe the enlargement.

   • enlargement, scale factor 3, centre (6, 1)
   • enlargement, scale factor 3, centre (0, 0)
   • enlargement, scale factor 3, centre (−6, 1)
   • enlargement, scale factor 2, centre (6, 1)
   Check

10. 10. The vertices of shape C are at (1, 1), (4, 1), (4, 6) and (1, 3). The vertices of shape D are at (−1, −2), (−1, 2), (5, −2) and (5, 8). Shape D is an enlargement of shape C. Describe the enlargement.

    • scale factor 2, centre (0, 0)
    • scale factor 3, centre (3, 4)
    • scale factor 2, centre (1, 1)
    • scale factor 2, centre (3, 4)
    Check

11. 11. Circle G is an enlargement of circle F. Describe the enlargement.

    • enlargement, scale factor 2, centre (0, 0)
    • enlargement, scale factor 2, centre (2, 4)
    • enlargement, scale factor 4, centre (2, 4)
    • enlargement, scale factor 2, centre (2, 2)
    Check

12. 12. Circle F has radius 2 cm. Use the formula C = πd to work out its circumference, to 1 decimal place.

    • 12.0 cm
    • 12.6 cm
    • 25.1 cm
    • 6.3 cm
    Check

13. 13. Circle F has circumference 4π cm. Circle G is an enlargement of F with scale factor 2. Use the scale factor to work out the circumference of circle G.

    • 16π cm
    • 6π cm
    • 8π cm
    • 4π cm
    Check

14. 14. Circle G has radius 4 cm. Use C = πd to check the circumference of circle G.

    • 32π cm
    • 16π cm
    • 8π cm
    • 4π cm
    Check

15. 15. Circle F has radius 2 cm. Use the formula A = πr² to work out its area.

    • 4π cm²
    • 16π cm²
    • 2π cm²
    • 8π cm²
    Check

16. 16. Circle F has area 4π cm². Circle G is an enlargement of F with scale factor 2. Use the scale factor to work out the area of circle G.

    • 8π cm²
    • 6π cm²
    • 64π cm²
    • 16π cm²
    Check

17. 17. Circle G has radius 4 cm. Use A = πr² to check the area of circle G.

    • 32π cm²
    • 64π cm²
    • 16π cm²
    • 8π cm²
    Check

18. 18. Triangle H is an enlargement of triangle K by a scale factor of 3. Triangle H has perimeter 36 cm and area 54 cm². Arun works out that the perimeter of triangle K is 108 cm. Is Arun correct?

    • Yes
    • No
    Check

19. 19. Triangle H is an enlargement of triangle K by a scale factor of 3. Triangle H has perimeter 36 cm and area 54 cm². What is the area of triangle K?

    • 6 cm²
    • 18 cm²
    • 162 cm²
    • 486 cm²
    Check