Reflection and translation – Year 5 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. Go across 2 and up 5: (2, 5).
   2. Across 6 and up 1: (6, 1).
   3. Across 4 and up 4: (4, 4).
   4. Count the steps along and up: A is 2 + 5 = 7 steps, B is 6 + 1 = 7 steps and C is 4 + 4 = 8 steps. So A and B are equally near and C is further.

2. Answer to Question 2

   1. The fourth corner is above (1, 1), so it is (1, 3).
   2. Along the bottom from x = 1 to x = 5 is 4 squares. Up the side from y = 1 to y = 3 is 2 squares. The sides are 4 and 2.
   3. Perimeter: 2 × (4 + 2) = 12. Area: 4 × 2 = 8 squares.

3. Answer to Question 3

   1. (2, 3): x = 2 + 4 = 6 and y = 3 + 2 = 5. The image is (6, 5).
   2. (7, 5): x = 7 − 3 = 4 and y = 5 − 4 = 1. The image is (4, 1).
   3. (1, 1): x = 1 + 6 = 7 and y = 1 + 0 = 1. The image is (7, 1).
   4. (4, 6): x = 4 − 2 = 2 and y = 6 − 5 = 1. The image is (2, 1).

4. Answer to Question 4

   1. (6, 3), (8, 3), (6, 6) (add 5 to x and 2 to y).
   2. (5, 1), (7, 1), (5, 4) (add 4 to x, y stays the same).
   3. Yes. A translation only slides the shape, so all sides and angles stay the same.

5. Answer to Question 5

   1. (2, 3) is 3 squares from the line, so the image is 3 on the other side: (8, 3).
   2. (4, 5) is 1 square from the line, so the image is 1 on the other side: (6, 5).
   3. (1, 2) is 4 squares from the line, so the image is 4 on the other side: (9, 2).
   4. (5, 1) is 0 squares from the line, so the image is 0 on the other side: (5, 1).

6. Answer to Question 6

   1. (2, 1) is 3 squares from the line, so the image is 3 on the other side: (2, 7).
   2. (3, 2) is 2 squares from the line, so the image is 2 on the other side: (3, 6).
   3. (5, 4) is 0 squares from the line, so the image is 0 on the other side: (5, 4). (It lies on the mirror line, so it does not move.)
   4. (1, 6) is 2 squares from the line, so the image is 2 on the other side: (1, 2).

7. Answer to Question 7

   1. From (1, 1) to (4, 3): 3 right and 2 up.
   2. From (4, 3) to (7, 2): 3 right and 1 down.
   3. (7 − 2, 2 + 3) = (5, 5).
   4. The cave.

8. Answer to Question 8

   1. Start (2, 2). Right 4: (6, 2). Up 3: (6, 5). Left 2: (4, 5). Down 1: (4, 4).
   2. The finish is (4, 4). 4 − 2 = 2 and 4 − 2 = 2, so 2 squares right and 2 squares up.
   3. The reverse: 2 squares left and 2 squares down.
   4. (4, 4) is 2 squares left of x = 6, so the image is 2 right: (8, 4).

9. Answer to Question 9

   1. 4 − 2 = 2 squares.
   2. 2 squares the other side: (6, 1).
   3. (6 − 3, 5 − 2) = (3, 3).
   4. Tom's reflected counter is at (6, 1) and Zara's is at (3, 3). They are not in the same place.

10. Answer to Question 10

    1. 7 − 4 = 3 squares.
    2. The top is 3 squares above the line, so the image is 3 below: 4 − 3 = 1. The image is at (4, 1).
    3. The base is on the mirror line, so it does not move: (4, 4).
    4. 3 + 3 = 6 squares.

11. Answer to Question 11

    1. 6 − 3 = 3 squares.
    2. Using 6 − x: (4, 2) → (2, 2); (6, 2) → (0, 2); (6, 5) → (0, 5); (4, 5) → (2, 5). The wing has corners (2, 2), (0, 2), (0, 5), (2, 5).
    3. (4, 2) and (4, 5) are both 1 square from the mirror line, and (6, 2) and (6, 5) are both 3 squares from it.

12. Answer to Question 12

    1. (3, 4) and (5, 4) lie on y = 4, so they do not move.
    2. (4, 6) is 2 above the line, so the image is 2 below: (4, 2).
    3. Top (4, 6), right (5, 4), bottom (4, 2), left (3, 4): (4, 6), (5, 4), (4, 2), (3, 4).
    4. From y = 6 down to y = 2 is 4 squares.

13. Answer to Question 13

    1. (7, 4), (9, 4), (9, 6), (7, 6).
    2. Area = 2 × 2 = 4 squares. It does not change because a translation keeps the size.
    3. Using 18 − x: (7, 4) → (11, 4); (9, 4) → (9, 4); (9, 6) → (9, 6); (7, 6) → (11, 6). The corners are (11, 4), (9, 4), (9, 6), (11, 6).

14. Answer to Question 14

    1. 6 − 0 = 6 squares.
    2. Reflected posts: (12, 3) and (12, 5).
    3. From x = 0 to x = 12 is 12 squares.
    4. (1, 3) and (1, 5).

15. Answer to Question 15

    1. Add 3 to x and 1 to y: A'(4, 3), B'(7, 3), C'(4, 6).
    2. New x = 16 − x: (4, 3) → (12, 3); (7, 3) → (9, 3); (4, 6) → (12, 6). The corners are (12, 3), (9, 3), (12, 6).
    3. Yes. Translations and reflections keep all lengths and angles the same.
    4. The translation 3 squares right and 1 square up.
    5. No. The reflection flips the triangle, so the right angle is now at the right-hand side instead of the left.

16. Answer to Question 16

    1. x: 8 − 3 = 5 and y: 6 − 4 = 2. The translation is 5 squares right and 2 squares up.
    2. (9 − 4, 7 − 5) = (5, 2).
    3. The image is 3 squares right of the line (8 − 5 = 3), so the original was 3 left: 5 − 3 = 2. The original point is (2, 2).
    4. The image is 2 below the line (3 − 1 = 2), so the original is 2 above: 3 + 2 = 5. The original point is (4, 5).
    5. The translation is 4 right and 1 up. (4, 2) → (8, 3) and (3, 5) → (7, 6).

17. Answer to Question 17

    1. New x = 10 − x: (1, 1) → (9, 1); (4, 1) → (6, 1); (4, 2) → (6, 2); (2, 2) → (8, 2); (2, 4) → (8, 4); (1, 4) → (9, 4).
    2. (4, 1) and (4, 2) are the closest: 5 − 4 = 1 square away.
    3. Subtract 1 from y: (9, 0), (6, 0), (6, 1), (8, 1), (8, 3), (9, 3).
    4. Yes, before the translation the two tiles form a symmetrical pattern, since each point and its image are the same distance from x = 5.

18. Answer to Question 18

    1. (8 − 2, 5 − 1) = 6 squares right and 4 squares up.
    2. From (2, 1), 3 right and 2 up gives (5, 3), which is the bench. The bench is at the halfway point of the path (half of 6 and 4), so yes.
    3. 8 is 3 right of the line, so the image is 3 left: (2, 5).
    4. (8 − 2, 5 − 4) = (6, 1).
    5. No. (2, 5) and (6, 1) are different points.

19. Answer to Question 19

    1. The sides are 3 and 2. Perimeter: 2 × (3 + 2) = 10. Area: 3 × 2 = 6 squares.
    2. New x = 12 − x: (1, 1) → (11, 1); (4, 1) → (8, 1); (4, 3) → (8, 3); (1, 3) → (11, 3).
    3. Add 2 to y: (11, 3), (8, 3), (8, 5), (11, 5).
    4. Perimeter 10 and area 6 squares, the same as the original. Reflections and translations do not change size.
    5. The corners (4, 1) and (4, 3) are nearest: 6 − 4 = 2 squares from the line.

20. Answer to Question 20

    1. P is 3 left of x = 5, so the image is 3 right: (8, 3).
    2. The point (8, 3) is on the line x = 8, so it does not move. The final image is (8, 3).
    3. From (2, 3) to (8, 3) is 6 squares right (no vertical move).
    4. The distance between the mirror lines is 8 − 5 = 3 squares, and the translation is 6 squares, which is twice the distance between the lines.