Coordinates and translation – Year 4 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. Point A is 3 across and 5 up: (3, 5).
   2. Point B is 6 across and 2 up: (6, 2).
   3. Point C is 0 across and 4 up: (0, 4).
   4. Point D is 7 across and 7 up: (7, 7).
   5. Point E is 5 across and 0 up: (5, 0).

2. Answer to Question 2

   1. R (0, 3) is on the vertical axis and T (6, 0) is on the horizontal axis: R and T.
   2. The biggest x-coordinate is 7: point Q.
   3. The biggest y-coordinate is 6: point P.
   4. No two points share a y-coordinate and no two share an x-coordinate in the list, so there is no such pair.

3. Answer to Question 3

   1. (1, 3): it has the x of (1, 1) and the y of (5, 3).
   2. (7, 2): x of (7, 6) and y of (2, 2).
   3. (0, 0): x of (0, 4) and y of (4, 0).
   4. (8, 5): x of (8, 2) and y of (3, 5).

4. Answer to Question 4

   1. Same y, so horizontal: 6 − 1 = 5 units.
   2. Same x, so vertical: 7 − 1 = 6 units.
   3. 9 − 0 = 9 units.
   4. Width 8 − 2 = 6, height 4 − 1 = 3. Perimeter 2 × (6 + 3) = 18 units. Area 6 × 3 = 18 square units.

5. Answer to Question 5

   1. (3, 4) 2 right and 1 up: x = 3 + 2 = 5, y = 4 + 1 = 5. New point (5, 5).
   2. (5, 2) 3 left and 4 up: x = 5 − 3 = 2, y = 2 + 4 = 6. New point (2, 6).
   3. (6, 7) 5 down: x = 6 + 0 = 6, y = 7 − 5 = 2. New point (6, 2).
   4. (1, 1) 6 right and 6 up: x = 1 + 6 = 7, y = 1 + 6 = 7. New point (7, 7).

6. Answer to Question 6

   1. x changes from 2 to 7 and y from 3 to 5: 5 right and 2 up.
   2. x changes from 6 to 2 and y from 6 to 2: 4 left and 4 down.
   3. x changes from 1 to 1 and y from 7 to 3: 4 down.
   4. x changes from 8 to 3 and y from 1 to 4: 5 left and 3 up.

7. Answer to Question 7

   1. The smallest x-coordinate is 2, so the cave (2, 7).
   2. From (3, 2) to (8, 3): 5 right and 1 up, which is 6 squares, or 60 paces.
   3. From (6, 5) to (2, 7): 4 left and 2 up.
   4. From (4, 6) to the palm tree (6, 5): 2 across and 1 down, 3 squares. To the cave (2, 7): 2 across and 1 up, 3 squares. They are the same distance, 3 squares.

8. Answer to Question 8

   1. (3, 2) is in the list, so it is a hit on the big ship.
   2. (2, 3) is not in the list (it is across 2, up 3, a different square), so it is a miss.
   3. The two squares (6, 5) and (6, 6) have the same x, so the ship is vertical.
   4. She must call (2, 2), (3, 2) and (4, 2) (all three).

9. Answer to Question 9

   1. The same row means the same y-coordinate (3): Bea.
   2. The same column means the same x-coordinate (2): Cal.
   3. The corner has the x of Bea (5) and the y of Cal (6): (5, 6).
   4. x = 2 + 3 = 5 and y = 3 + 2 = 5, so Ali sits at (5, 5).

10. Answer to Question 10

    1. (1 + 4, 1 + 3) = (5, 4).
    2. Left 2: (3, 4). Up 2: (3, 6). Right 5: (8, 6).
    3. From (8, 6) to (1, 1): 7 left and 5 down: left 7, down 5.
    4. 4 + 3 + 2 + 2 + 5 = 16 squares.

11. Answer to Question 11

    1. Same y, so 4 − 1 = 3 squares.
    2. Same x, so 6 − 2 = 4 squares.
    3. Same y, so 8 − 4 = 4 squares.
    4. 3 + 4 + 4 = 11 squares. 11 × 200 = 2 200 m (2.2 km).

12. Answer to Question 12

    1. A′ = (1 + 3, 1 + 2) = (4, 3); B′ = (4 + 3, 1 + 2) = (7, 3); C′ = (1 + 3, 3 + 2) = (4, 5).
    2. The opposite movement: 3 left and 2 down.
    3. From (4, 3): x = 4 + 2 = 6 and y = 3 − 1 = 2. A″ = (6, 2).
    4. Base AB = 4 − 1 = 3 and height AC = 3 − 1 = 2. Half of 3 × 2 = 3 square units. A translation does not change the area.

13. Answer to Question 13

    1. Length 7 − 1 = 6 m, width 5 − 1 = 4 m.
    2. 2 × (6 + 4) = 20 m.
    3. Garden 6 × 4 = 24 m². Pond: (5 − 3) × (4 − 2) = 2 × 2 = 4 m².
    4. 24 − 4 = 20 m².

14. Answer to Question 14

    1. From (2, 2) to (5, 2): 3 squares to the right.
    2. From (5, 2) to (8, 5): 3 right and 3 up.
    3. 3 + 3 + 3 = 9 squares.
    4. Going up first from (5, 2) he passes (5, 3), (5, 4) and (5, 5), which is where the dragon is. Going right first he moves along y = 2 to (8, 2) and then up to (8, 5), and the dragon at (5, 5) is not on this route. So right first avoids the dragon.

15. Answer to Question 15

    1. D has the x of A (2) and the y of C (4): (2, 4).
    2. Width 7 − 2 = 5 and height 4 − 1 = 3. Perimeter 2 × (5 + 3) = 16 units. Area 5 × 3 = 15 square units.
    3. Subtract 1 from each x and add 3 to each y: A′ (1, 4), B′ (6, 4), C′ (6, 7), D′ (1, 7).
    4. The width is 5 and half of 5 is 2.5 units.
    5. Yes, the halves are identical (mirror images). The rectangle has 2 lines of symmetry.

16. Answer to Question 16

    1. 3 across and 2 up: 3 + 2 = 5 squares.
    2. A to B: 6 − 2 = 4. B to C: 7 − 3 = 4. C to D: 6 − 1 = 5. Total 4 + 4 + 5 = 13 squares.
    3. 5 + 13 = 18 squares. 18 × 100 = 1 800 m.
    4. D (7, 1) to (0, 0): 7 + 1 = 8 squares.
    5. 18 + 8 = 26 squares. 26 × 8p = 208p = £2.08.

17. Answer to Question 17

    1. Vertical (same x): (2, 1)–(2, 7), (4, 7)–(4, 3), (7, 3)–(7, 1). Horizontal (same y): (2, 7)–(4, 7), (4, 3)–(7, 3), (7, 1)–(2, 1).
    2. Sides: 6 + 2 + 4 + 3 + 2 + 5 = 22 units. (Check: 2 × (5 + 6) = 22.)
    3. Tall part: 2 × 6 = 12. Foot: 3 × 2 = 6 (from x = 4 to 7 and y = 1 to 3). Total 18 square units.
    4. Subtract 2 from x and 1 from y: (0, 0), (0, 6), (2, 6), (2, 2), (5, 2), (5, 0).
    5. All coordinates are between 0 and 8, so yes; the letter now touches the axes.

18. Answer to Question 18

    1. x: 1 to 6 is 5 right; y: 5 to 7 is 2 up. 5 right and 2 up.
    2. x: 1 to 6 is 5 right; y: 5 to 3 is 2 down. 5 right and 2 down.
    3. H to V: 5 + 2 = 7 squares. V to B: 9 − 6 = 3 squares. Total 10 squares.
    4. L (6, 7) → (6 − 2, 7 − 4) = (4, 3). The path goes across from (1, 5) to (6, 5) and then down to (6, 3), so (4, 3) is not on the path.
    5. 10 × 50 = 500 m.

19. Answer to Question 19

    1. (1, 1) is 4 from the line, so its reflection is 4 on the other side: (9, 1). (1, 4) → (9, 4). (3, 6) is 2 from the line → (7, 6).
    2. Going round: (1, 1), (9, 1), (9, 4), (7, 6), (3, 6), (1, 4).
    3. The width is 9 − 1 = 8 units.
    4. The whole flag has 1 line of symmetry (x = 5).
    5. The top corners (3, 6) and (7, 6) become (6, 8) and (10, 8).

20. Answer to Question 20

    1. The other corners are at (6, 2) and (2, 6): B (6, 2) and D (2, 6).
    2. Side 6 − 2 = 4. Area 4 × 4 = 16 square units.
    3. If we do not need the sides to be parallel to the axes, there is only one square with those two opposite corners, because the diagonals of a square cross in the middle at 90° and are equal. Here the diagonal AC goes up-right, so the other diagonal goes up-left through (4, 4), and its ends are (2, 6) and (6, 2). So the answer is no, only one square.