First steps in coordinates · Ages 12–13
Translation
Left and right change x; up and down change y.
How to do it
Method
Left and right change x; up and down change y
(−2, 3), 5 right and 4 down: (3, −1)
Another way
Count squares
Every corner moves the same squares
In full
A translation moves a whole shape the same distance in the same direction; its shape, size and the way it faces don't change. Right h units: add h to x; left: take h from x. Up k units: add k to y; down: take k from y. The other coordinate stays. (−2, 3) moved 5 units right is (3, 3), and then 4 units down, (3, −1). To find the point from its image, go back the other way. Or count squares on the grid: every corner moves the same number of squares.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Translating (−4, 4) 6 units down gives (, ).
Fill in each blank
Show the answer and working
Answer: −4, −2
Down: take 6 from y, 4 − 6 = −2; x stays.
Example 2
Translating (9, −5) 5 units to the right gives (, ).
Fill in each blank
Show the answer and working
Answer: 14, −5
To the right: add 5 to x, 9 + 5 = 14; y stays.
Example 3
Where does (6, −5) go when translated 4 units to the left?
- A. (2, −5)
- B. (6, −9)
- C. (10, −5)
- D. (2, −9)
Choose the right answer
Show the answer and working
Answer: A. (2, −5)
4 units left: take 4 from x, 6 − 4 = 2; y stays: (2, −5).
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Translating (1, −3) 2 units down gives (, ).
Fill in each blank
Answer:
2.Translating (1, 7) 2 units to the right gives (, ).
Fill in each blank
Answer:
3.Triangle ABC is translated 5 units to the right, to A′B′C′. Which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:
4.Segment AB runs from A(5, −2) to B(−2, −5). Translated 3 units left, then 2 units up, it becomes A′(, ) and B′(, ).
Fill in each blank
Answer:
5.A(5, 0) is translated to A′(6, −6). What is the translation?
- A. 1 unit left, then 6 units down
- B. 1 unit right, then 6 units up
- C. 6 units right, then 1 unit down
- D. 1 unit right, then 6 units down
Choose the right answer
Answer:
All the answers
- 1. 1, −5
- 2. 3, 7
- 3. C
- 4. 2, 0, −5, −3
- 5. D. 1 unit right, then 6 units down
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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