Shape and space · Ages 9–10

Translations worksheet

Part of: Coordinates and moving shapes

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Shape and space · Ages 9–10

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

1.The point (2, 2) moves 1 squares right and 1 squares up. Its new position is (, ).
Fill in each blank
Answer:
2.Shape Q is shape P after a translation. P moved squares right and squares up.
Fill in each blank
Answer:
3.The point (2, 5) moves 3 squares right and 3 squares up. Its new position is (, ).
Fill in each blank
Answer:
4.The point (0, 0) moves 2 squares right and 3 squares up. Its new position is (, ).
Fill in each blank
Answer:
5.A translation moves A (5, 7) to A′ (1, 7). The same translation moves B (8, 1) to B′ (, ).
Fill in each blank
Answer:
6.A translation moves A (5, 1) to A′ (2, 3). The same translation moves B (5, 3) to B′ (, ).
Fill in each blank
Answer:

13.A row of paper-cut patterns: the 1st one's bottom left corner is at (3, 2), and each one after is the one before moved 2 squares right. What is the x-coordinate of the bottom left corner of pattern 4?
Working:
Answer:
14.A rectangular puzzle piece lies on a grid board, its bottom left corner at (4, 4) and its top right corner at (6, 5). Ka-yee slides it 4 squares right and 1 squares up without turning it. Its top right corner is now at (, ).
Fill in each blank
Working:
Answer:
15.In a game, Ka-yan's character starts at (4, 7), goes 3 squares left, then 2 down, then 2 right. It is now at (, ).
Fill in each blank
Working:
Answer:
16.A crane at the container port slides a container: its bottom left corner moves from (1, 6) to (7, 5). The container moved squares right and squares down.
Fill in each blank
Working:
Answer:
17.A row of paper-cut patterns: the 1st one's bottom left corner is at (1, 2), and each one after is the one before moved 2 squares right. What is the x-coordinate of the bottom left corner of pattern 5?
Working:
Answer:
18.A rectangular puzzle piece lies on a grid board, its bottom left corner at (4, 1) and its top right corner at (8, 3). May slides it 1 squares right and 1 squares up without turning it. Its top right corner is now at (, ).
Fill in each blank
Working:
Answer:

Show the answers and working

Translations worksheet: Answers and working

1. 3, 3
Right adds to x, up adds to y. Start from (2, 2).
Right adds 1 to x: 3. Up adds 1 to y: 3.
2. 2, 2
Pick one corner, say the right angle, find it on P and on Q, then count how far it moved.
Follow one corner: the right angle moves from (4, 2) to (6, 4), 2 right and 2 up.
3. 5, 8
Right adds to x, up adds to y. Start from (2, 5).
Right adds 3 to x: 5. Up adds 3 to y: 8.
4. 2, 3
Right adds to x, up adds to y. Start from (0, 0).
Right adds 2 to x: 2. Up adds 3 to y: 3.
5. 4, 1
First see how A moved: x went from 5 to 1 and y from 7 to 7. By how much each?
A's x goes from 5 to 1 and y from 7 to 7; B changes the same way: (4, 1).
6. 2, 5
First see how A moved: x went from 5 to 2 and y from 1 to 3. By how much each?
A's x goes from 5 to 2 and y from 1 to 3; B changes the same way: (2, 5).

7. D
Move one corner first: the right angle 3 left and 1 up. Then check the triangle hasn't been flipped.
Every corner moves 3 left and 1 up; the shape and the way it faces stay the same.
8. D. 5 right, 2 down
Follow the right angle from P to Q and count how far it went, not the gap between the shapes.
The right angle moves from (3, 4) to (8, 2): 5 right, 2 down.
9. False
Check two things: did the right angle move exactly 2 right, and does the triangle still face the same way?
Q would be every corner of P moved 2 right, with the shape facing the same way.
10. D
Move one corner first: the right angle 1 left and 3 up. Then check the triangle hasn't been flipped.
Every corner moves 1 left and 3 up; the shape and the way it faces stay the same.
11. True
Check two things: did the right angle move exactly 3 right, and does the triangle still face the same way?
Q would be every corner of P moved 3 right, with the shape facing the same way.
12. False
Check two things: did the right angle move exactly 5 right, and does the triangle still face the same way?
Q would be every corner of P moved 5 right, with the shape facing the same way.

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

13. 9
How many moves are there from the 1st pattern to pattern 4? Careful: not 4.
From the 1st to number 4 is 3 moves: 3 + 3 × 2 = 9.
14. 10, 6
A slide moves every corner the same, so you only need the top right corner, (6, 5).
A slide moves every corner the same: the top right (6, 5) goes 4 right and 1 up, to (10, 6).
15. 3, 5
Left and right change only x; up and down change only y. Do them apart: x goes 3 left, then 2 right.
x: 4 − 3 + 2 = 3; y: 7 − 2 = 5.
16. 6, 1
Compare the two x's, 1 and 7; then the two y's, 6 and 5.
x goes from 1 to 7: 6 right. y goes from 6 to 5: 1 down.
17. 9
How many moves are there from the 1st pattern to pattern 5? Careful: not 5.
From the 1st to number 5 is 4 moves: 1 + 4 × 2 = 9.
18. 9, 4
A slide moves every corner the same, so you only need the top right corner, (8, 3).
A slide moves every corner the same: the top right (8, 3) goes 1 right and 1 up, to (9, 4).

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