Coordinates and trigonometry · Ages 12–13

Translation worksheet

Part of: First steps in coordinates

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Coordinates and trigonometry · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Translating (9, −6) 6 units down gives (, ).
Fill in each blank
Answer:
2.Translating (8, −2) 2 units to the right gives (, ).
Fill in each blank
Answer:
3.Translating (3, 1) 2 units to the right gives (, ).
Fill in each blank
Answer:
4.Translating (−8, 1) 7 units down gives (, ).
Fill in each blank
Answer:
5.(−5, −5) is translated 1 unit right, then 2 units up. Its image is (, ).
Fill in each blank
Answer:
6.Translated 4 units up, P goes to (−8, −2). P's y-coordinate is .
Answer:
7.Translated 2 units up, P goes to (5, −9). P's y-coordinate is .
Answer:
8.Segment AB runs from A(2, −3) to B(2, 1). Translated 5 units left, then 2 units up, it becomes A′(, ) and B′(, ).
Fill in each blank
Answer:

13.P is translated 6 units right, then 2 units down, and lands at (2, 3). What is P's x-coordinate?
Working:
Answer:
14.After a translation, corner A(−5, −5) goes to A′(−4, −2), and another corner B goes to B′(3, −3). What is B's y-coordinate?
Working:
Answer:
15.Rectangle ABCD is translated 3 units left, then 3 units up, to A′B′C′D′, with A′(−5, 5) and C′(−3, 7). The original A is (, ) and C is (, ).
Fill in each blank
Working:
Answer:
16.A(5, −5) is translated to A′(9, −6). The translation is units right, then units down.
Fill in each blank
Working:
Answer:
17.In a video game a character is at (4, −4). Press → 5 times, then ↓ 6 times, one square each. It is now at (, ).
Fill in each blank
Working:
Answer:
18.A translation moves A(1, −1) to A′(−3, −2). Where does the same translation take B(−4, 2)?
- A. (−8, 1)
- B. (−8, 2)
- C. (−5, −2)
- D. (0, 3)
Choose the right answer
Working:
Answer:

Show the answers and working

Translation worksheet: Answers and working

1. 9, −12
Down: take 6 from y, −6 − 6 = −12; x stays.
2. 10, −2
To the right: add 2 to x, 8 + 2 = 10; y stays.
3. 5, 1
To the right: add 2 to x, 3 + 2 = 5; y stays.
4. −8, −6
Down: take 7 from y, 1 − 7 = −6; x stays.
5. −4, −3
Right: add 1 to x, −5 + 1 = −4; up: add 2 to y, −5 + 2 = −3.
6. −6
Go back the other way: 4 units down from the image, −2 − 4 = −6.
7. −11
Go back the other way: 2 units down from the image, −9 − 2 = −11.
8. −3, −1, −3, 3
Every point alike: take 5 from x, add 2 to y. A′(−3, −1), B′(−3, 3).

9. D. (0, −1)
1 unit left: take 1 from x, 1 − 1 = 0; y stays: (0, −1).
10. C
Every corner moves 5 squares right: add 5 to x, y stays. The image keeps its shape, size and direction.
11. C. 4 units right, then 5 units down
x: 3 → 7, up by 4, so 4 right; y: 1 → −4, down by 5, so 5 down.
12. B. 5 units right, then 2 units down
x: −6 → −1, up by 5, so 5 right; y: −1 → −3, down by 2, so 2 down.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. −4
Undo it: 6 units left, 2 − 6 = −4. The up-or-down move doesn't touch x.
14. −6
A to A′ takes y from −5 to −2; B's y changes by as much. Back from B′: −3 − (−2 − −5) = −6.
15. −2, 2, 0, 4
Go back from the image: 3 right (add 3 to x) and 3 down (take 3 from y). A(−2, 2), C(0, 4).
16. 4, 1
x rises from 5 to 9, by 4: 4 right; y falls from −5 to −6, by 1: 1 down.
17. 9, −10
5 right: add 5 to x, 4 + 5 = 9; 6 down: take 6 from y, −4 − 6 = −10.
18. A. (−8, 1)
A → A′: x from 1 to −3, y from −1 to −2. B's coordinates change the same way: (−8, 1).

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