Math 7 · Unit 14: Position and transformation · Cambridge Lower Secondary Maths Stage 7

Questions

1. 1. Triangle ABC from the first example in the introduction, is translated 5 squares right. Copy and complete the workings to find the coordinates of the vertices of the image A′B′C′.

   Fill the blanks with these.

   • 6
   • 8
   • 9
   • −2
   Check

2. 2. Triangle ABC from the first example in the introduction, is translated 3 squares left. Copy and complete the workings to find the coordinates of the vertices of the image A′B′C′.

   Fill the blanks with these.

   • 0
   • 6
   • 1
   • 7
   Check

3. 3. A square, ABCD, has vertices at the points A(5, 3), B(8, 3), C(8, 6) and D(5, 6). ABCD is translated 4 squares left. The image of ABCD is A′B′C′D′. Copy and complete the workings to find the coordinates of the vertices of A′B′C′D′.

   Fill the blanks with these.

   • 12
   • 1
   • 9
   • 4
   Check

4. 4. Triangle DEF from the second example in the introduction, is translated 1 square up. Copy and complete the workings to find the coordinates of the vertices of the image D′E′F′.

   Fill the blanks with these.

   • 2
   • 4
   • 3
   Check

5. 5. Triangle DEF from the second example in the introduction, is translated 2 squares down. Copy and complete the workings to find the coordinates of the vertices of the image D′E′F′.

   Fill the blanks with these.

   • 1
   • 3
   • 5
   Check

6. 6. A rectangle, ABCD, has vertices at the points A(2, 7), B(6, 7), C(6, 9) and D(2, 9). ABCD is translated 4 squares down. The image of ABCD is A′B′C′D′. Copy and complete the workings to find the coordinates of the vertices of A′B′C′D′.

   Fill the blanks with these.

   • 3
   • 13
   • 11
   • 5
   Check

7. 7. A triangle, PQR, has vertices at the points P(4, 5), Q(7, 5) and R(6, 9). PQR is translated 3 squares right and 4 squares up. The image of PQR is P′Q′R′. Copy and complete the workings to find the coordinates of the vertices of P′Q′R′.

   Fill the blanks with these.

   • 9
   • 4
   • 13
   • 1
   • 10
   Check

8. 8. A rectangle, ABCD, has vertices at the points A(4, 8), B(8, 8), C(8, 10) and D(4, 10). ABCD is translated 1 square left and 5 squares down. The image of ABCD is A′B′C′D′. Copy and complete the workings to find the coordinates of the vertices of A′B′C′D′.

   Fill the blanks with these.

   • 9
   • 5
   • 13
   • 7
   • 3
   Check

9. 9. Match each translation to what you add or subtract. The x-coordinate changes for left and right, the y-coordinate for up and down.

   • 6 squares right and 3 squares down
   • 6 squares left and 3 squares up
   • 6 squares left and 3 squares down
   • 6 squares right and 3 squares up

   • x − 6, y − 3
   • x + 6, y + 3
   • x + 6, y − 3
   • x − 6, y + 3
   Check

10. 10. Question 10: rhombus PQRS has P(6, 2), Q(7, 4), R(6, 6) and S(5, 4). It is translated 3 squares left and 2 squares down. What are the coordinates of P′Q′R′S′?

    • P′(4, −1), Q′(5, 1), R′(4, 3), S′(3, 1)
    • P′(3, 0), Q′(4, 2), R′(3, 4), S′(2, 2)
    • P′(3, 0), Q′(4, 2), R′(3, 4), S′(2, 4)
    • P′(9, 4), Q′(10, 6), R′(9, 8), S′(8, 6)
    Check

11. 11. Question 11: AB goes from A(4, 7) to B(9, 3). It is translated 3 squares left and 2 squares down. Ivan says A′ is (7, 5) and B′ is (12, 1). What mistake has he made?

    • He made no mistake.
    • He swapped the x- and y-coordinates.
    • He added 3 to the x-coordinates instead of subtracting 3.
    • He subtracted 2 instead of adding 2.
    Check

12. 12. Question 11b: AB goes from A(4, 7) to B(9, 3). It is translated 3 squares left and 2 squares down. What are the correct coordinates of A′ and B′?

    • A′(1, 5), B′(6, 1)
    • A′(2, 4), B′(7, 0)
    • A′(7, 5), B′(12, 1)
    • A′(1, 9), B′(6, 5)
    Check

13. 13. Ivan's homework: AB goes from A(4, 7) to B(9, 3). It is translated 3 squares left and 2 squares down. Ivan says A′ is (7, 5) and B′ is (12, 1), which is incorrect. How could Ivan check his answers?

    • Move A′ and B′ back the opposite way, 3 squares right and 2 squares up, and see if they land on A and B
    • Check that the x- and y-coordinates of A′ are swapped compared with A
    • Check that A′B′ is longer than AB
    • Check that A′ and B′ have the same coordinates as A and B
    Check

14. 14. Question 12: Simone translates triangle XYZ, with X(5, 4), Y(8, 5) and Z(6, 9), to X′(2, 7), Y′(5, 8) and Z′(3, 12). Which translation has she used?

    • 3 squares left and 3 squares up
    • 3 squares right and 3 squares up
    • 3 squares left and 3 squares down
    • 3 squares right and 3 squares down
    Check

15. 15. Question 13: Alya translates kite JKLM, with J(1, 5), K(4, 4), L(1, −1) and M(−2, 4). She says J′(−2, 4), K′(1, 3), L′(−2, 2) and M′(−5, 3). Which vertex is incorrect?

    • M′: it should be (−5, 5).
    • J′: it should be (−2, 6).
    • L′: it should be (−2, −2).
    • K′: it should be (1, 5).
    Check

16. 16. A rectangle, CDEF, has vertices at the points C(2, −1), D(6, −1), E(6, −3) and F(2, −3). Nadim translates CDEF four times, using four different translations: A 5 squares right and 3 squares up, B 4 squares right and 2 squares down, C 4 squares left, D 3 squares left and 1 square down. After which translation will the object and the image be touching end to end?

    • 4 squares left
    • 5 squares right and 3 squares up
    • 3 squares left and 1 square down
    • 4 squares right and 2 squares down
    Check

17. 17. A rectangle, CDEF, has vertices at the points C(2, −1), D(6, −1), E(6, −3) and F(2, −3). Nadim translates CDEF four times, using four different translations: A 5 squares right and 3 squares up, B 4 squares right and 2 squares down, C 4 squares left, D 3 squares left and 1 square down. After which translation will the object and the image be touching corner to corner?

    • 3 squares left and 1 square down
    • 4 squares right and 2 squares down
    • 5 squares right and 3 squares up
    • 4 squares left
    Check

18. 18. A rectangle, CDEF, has vertices at the points C(2, −1), D(6, −1), E(6, −3) and F(2, −3). Nadim translates CDEF four times, using four different translations: A 5 squares right and 3 squares up, B 4 squares right and 2 squares down, C 4 squares left, D 3 squares left and 1 square down. After which translation will the object and the image be overlapping?

    • 5 squares right and 3 squares up
    • 4 squares right and 2 squares down
    • 4 squares left
    • 3 squares left and 1 square down
    Check

19. 19. A rectangle, CDEF, has vertices at the points C(2, −1), D(6, −1), E(6, −3) and F(2, −3). Nadim translates CDEF four times, using four different translations: A 5 squares right and 3 squares up, B 4 squares right and 2 squares down, C 4 squares left, D 3 squares left and 1 square down. After which translation will the object and the image be not touching or overlapping?

    • 4 squares right and 2 squares down
    • 3 squares left and 1 square down
    • 5 squares right and 3 squares up
    • 4 squares left
    Check

20. 20. Question 15a: Jon translates shape L 3 squares right and 2 squares up to M, then M 4 squares right and 6 squares up to N. What single translation takes L to N?

    • 12 squares right and 12 squares up
    • 7 squares right and 8 squares up
    • 1 square right and 4 squares up
    • 7 squares right and 4 squares up
    Check