Shape and space · Ages 9–10

Rotations worksheet

Part of: Coordinates and moving shapes

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Shape and space · Ages 9–10

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

1.Triangle ABC turns 90° clockwise about corner A. What is the x-coordinate of C′, C's new position?
Answer:
2.Triangle ABC turns 90° anticlockwise about corner A. B moves to B′ at (, ).
Fill in each blank
Answer:
3.The point (2, 10) turns 180° about (3, 5). Its new position is (, ).
Fill in each blank
Answer:
4.The point (0, 10) turns 180° about (4, 6). Its new position is (, ).
Fill in each blank
Answer:
5.The point (1, 1) turns 180° about (2, 2). Its new position is (, ).
Fill in each blank
Answer:
6.The point (1, 2) turns 180° about (2, 4). Its new position is (, ).
Fill in each blank
Answer:

7.The orange triangle turns 90° clockwise about corner A. Which picture shows the turned triangle (blue) correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
8.A clock's minute hand points at 6 and turns 90° (a quarter turn) clockwise about the centre. Which number does it point at now?
- A. 9
- B. 3
- C. 12
- D. 6
Choose the right answer
Answer:
9.A clock's minute hand points at 12 and turns 90° (a quarter turn) clockwise about the centre. Which number does it point at now?
- A. 6
- B. 9
- C. 12
- D. 3
Choose the right answer
Answer:
10.The blue triangle is the orange one turned 180° about A.
True or false?
Answer:
11.How is the blue triangle made from the orange one?
- A. Turned 90° clockwise about A
- B. Turned 180° about A
- C. Flipped in the upright line through A (a reflection)
- D. Turned 90° anticlockwise about A
Choose the right answer
Answer:
12.The orange triangle turns 180° (a half turn) about corner B. Which picture shows the turned triangle (blue) correctly?
- A
- B
- C
- D
Choose the right picture
Answer:

13.On a floor plan, a door's hinge is at (2, 3). Shut, the door's other end is at (4, 3). The door swings 90° anticlockwise about the hinge; its other end is now at (, ).
Fill in each blank
Working:
Answer:
14.A clock's minute hand points to 12. It turns 90° clockwise about the centre 1 times. Which number does it point to now?
Working:
Answer:
15.In a block game, Tsz-ching turns a block 90° clockwise 5 times. What is the fewest more clockwise turns that bring it back to how it started?
Working:
Answer:
16.On a floor plan, a door's hinge is at (2, 2). Shut, the door's other end is at (6, 2). The door swings 90° anticlockwise about the hinge; its other end is now at (, ).
Fill in each blank
Working:
Answer:
17.In a block game, May turns a block 90° clockwise 3 times. What is the fewest more clockwise turns that bring it back to how it started?
Working:
Answer:
18.In a block game, Tsz-ching turns a block 90° clockwise 7 times. What is the fewest more clockwise turns that bring it back to how it started?
Working:
Answer:

Show the answers and working

Rotations worksheet: Answers and working

1. 5
A stays put. AC points 1 up; turning 90° clockwise, which way does “up” become?
AC points 1 up; clockwise 90° turns “up” into “right”: C′ is 1 right of A, so x is 4 + 1 = 5.
2. 7, 4
A stays put. AB points 1 right; turning 90° anticlockwise, which way does “right” become?
AB points 1 right; anticlockwise 90° turns “right” into “up”: B′ is 1 above A, (7, 4).
3. 4, 0
In a half turn the centre (3, 5) is exactly halfway. See how far x goes from 2 to 3, then go as far again.
After a half turn the centre is exactly halfway between the point and its new place: x is 2 × 3 − 2 = 4, y is 2 × 5 − 10 = 0.
4. 8, 2
In a half turn the centre (4, 6) is exactly halfway. See how far x goes from 0 to 4, then go as far again.
After a half turn the centre is exactly halfway between the point and its new place: x is 2 × 4 − 0 = 8, y is 2 × 6 − 10 = 2.
5. 3, 3
In a half turn the centre (2, 2) is exactly halfway. See how far x goes from 1 to 2, then go as far again.
After a half turn the centre is exactly halfway between the point and its new place: x is 2 × 2 − 1 = 3, y is 2 × 2 − 1 = 3.
6. 3, 6
In a half turn the centre (2, 4) is exactly halfway. See how far x goes from 1 to 2, then go as far again.
After a half turn the centre is exactly halfway between the point and its new place: x is 2 × 2 − 1 = 3, y is 2 × 4 − 2 = 6.

7. A
A stays put. Take the side pointing right from A: where does it point after a quarter turn clockwise?
A quarter turn clockwise about A: the side pointing right now points down, and the side pointing up now points right.
8. A. 9
Clockwise is the way a clock's hands go. How many big steps is a quarter turn?
90° clockwise is a quarter turn, 3 big steps round the face: from 6 to 9.
9. D. 3
Clockwise is the way a clock's hands go. How many big steps is a quarter turn?
90° clockwise is a quarter turn, 3 big steps round the face: from 12 to 3.
10. False
A stays put. Check each side from A in the blue triangle: does each point exactly the opposite way?
After a half turn the side pointing right points left, and the side pointing up points down.
11. A. Turned 90° clockwise about A
Look at just the side pointing right from A: which way does it point in the blue triangle?
See where the two sides from A, which pointed right and up, point now.
12. C
B stays put and is still a corner afterwards. See where the side from B points after a half turn.
A half turn about B: B stays put, the side pointing left now points right, and what was above is now below.

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

13. 2, 5
The hinge stays put; the door is 2 squares long and points right. A quarter turn anticlockwise turns “right” into which way?
The door is 2 squares long and pointed right; turned 90° anticlockwise it points up: (2, 5).
14. 3
Each 90° is a quarter of the way round. Start at 12 and go round one turn at a time.
Each 90° is a quarter turn, 3 numbers on: 12 → 3 → 6 → 9 → 12 …; after 1 it points to 3.
15. 3 turns
Four 90° turns make a full turn. After 5 turns, how many short of the next full turn are you?
Four 90° turns make a full turn; 5 turns and 3 more make whole full turns.
16. 2, 6
The hinge stays put; the door is 4 squares long and points right. A quarter turn anticlockwise turns “right” into which way?
The door is 4 squares long and pointed right; turned 90° anticlockwise it points up: (2, 6).
17. 1 turn
Four 90° turns make a full turn. After 3 turns, how many short of the next full turn are you?
Four 90° turns make a full turn; 3 turns and 1 more make whole full turns.
18. 1 turn
Four 90° turns make a full turn. After 7 turns, how many short of the next full turn are you?
Four 90° turns make a full turn; 7 turns and 1 more make whole full turns.

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