Rotating shapes
The Maths Habit
How many squares from the cross to P? Which way?
The grey shape is pinned at the cross and turned. Which pink shape shows where it ends up?
C. It has turned about the pin. A has slid and B has flipped.
- Rotate
- Turn a shape about a point.
- Centre of rotation
- The point the shape turns about. Here it is the cross.
- 180°
- A half turn. The shape ends up upside down.
- 90° clockwise
- A quarter turn, the way the hands of a clock go.
- Count the squares from the cross to P.Say which way: up, down, left or right.
- Turn. Count the same squares the new way.180° is a half turn: the opposite way. Up and down swap, left and right swap. Mark P′.
- Trace the shape and the cross. Hold the cross with your pencil. Turn the paper.Check P lands on P′. Draw the new shape.
Use tracing paper to check.
- 1Trace
- Trace the shape and the cross.
- 2Turn
- Hold the cross with your pencil. Turn the paper a half turn.
- 3Draw
- Draw the new shape where the tracing lands.
Rotate the shape 180° about the cross.
Rotate the shape 180° about the cross.
Rotate the shape 180° about the cross.
Rotate the shape 180° about the cross.
Rotate the shape 180° about the cross.
Rotate the shape 180° about the cross.
Rotate the shape 180° about the cross.
Rotate the shape 180° about the cross.
Copy each shape. Rotate it 180° about the cross.
The pink arrow makes a quarter turn clockwise. Which way does it point now?
- Count the squares from the cross to P.Say which way: up, down, left or right.
- Turn. Count the same squares the new way.90° clockwise is a quarter turn: up goes to right, right to down, down to left, left to up. Mark P′.
- Trace the shape and the cross. Hold the cross with your pencil. Turn the paper.Check P lands on P′. Draw the new shape.
Use tracing paper to check.
- 1Trace
- Trace the shape and the cross.
- 2Turn
- Hold the cross with your pencil. Turn the paper a quarter turn clockwise.
- 3Draw
- Draw the new shape where the tracing lands.
Rotate the shape 90° clockwise about the cross.
Rotate the shape 90° clockwise about the cross.
Rotate the shape 90° clockwise about the cross.
Rotate the shape 90° clockwise about the cross.
Rotate the shape 90° clockwise about the cross.
Rotate the shape 90° clockwise about the cross.
Rotate the shape 90° clockwise about the cross.
Rotate the shape 90° clockwise about the cross.
Copy each shape. Rotate it 90° clockwise about the cross.
Is the pink shape the turn asked for? Thumbs up or thumbs down.
Answer sheet
The point (4, 2) is rotated 180° about (0, 0). Where does it end up?
(−4, −2)A shape is rotated 90° clockwise, then 90° clockwise again about the same cross. What single turn does the same?
180°, a half turnWhich clockwise turn does the same as 90° anticlockwise?
270° clockwise
Rotate the shape 180°. CountP2up/down/left/rightTurnP′2up/down/left/rightDraw
Rotate the shape 90° clockwise. CountP2up/down/left/rightTurnP′2up/down/left/rightDraw
Rotate the shape 90° clockwise. (Draw it on your ticket.)