Position and transformation
Rotating shapes
Rotating turns a shape about a fixed point. To describe a rotation fully you need three things: the centre, the angle, and which way round.
The centre of rotation
When you ROTATE a shape you turn it about a fixed point called the CENTRE OF ROTATION. The centre can be a vertex of the shape, a point inside it, or a point somewhere else entirely on the grid. Everything else swings around that point. The centre itself never moves.
Three things to state
A rotation is only fully described when you give all three: 1. The CENTRE of rotation. 2. The ANGLE — usually 90° or 180°. 3. The DIRECTION — CLOCKWISE or ANTICLOCKWISE. Miss one out and the answer is ambiguous. 'Rotate 90°' could send the shape either way.
The 180° special case
For a 180° turn you do not need the direction. Half a turn clockwise and half a turn anticlockwise land in exactly the same place — so 'rotate 180° about C' is complete on its own. For 90° the direction always matters.
Doing it with tracing paper
The reliable method: 1. Trace the shape onto tracing paper. 2. Put your pencil point on the centre of rotation and hold it there. 3. Turn the paper by the angle, in the right direction. 4. Mark where the image lands, then draw it on the grid. The object and image are always CONGRUENT — turning changes position and orientation, never size.
Worked examples
What must a rotation state?
- A turn needs a fixed point to turn about.
- It needs a size of turn.
- And it needs a direction.
Answer: The centre, the angle and the direction
Rotating 90° clockwise about C
- Trace the shape and hold the pencil on C.
- Turn the tracing paper a quarter turn clockwise.
- Mark and draw the image.
Answer: The image sits a quarter turn round from the object
Why 180° needs no direction
- 180° is half a full turn.
- Half a turn each way ends in the same place.
Answer: Clockwise and anticlockwise give the same image
Is the image the same size?
- A rotation turns the shape about a point.
- It does not stretch or shrink anything.
Answer: Yes — object and image are congruent
How many degrees in a quarter turn?
- A full turn is 360°.
- 360 ÷ 4 = 90.
Answer: 90°
Two 90° clockwise turns in a row
- 90 + 90 = 180.
- That is half a full turn.
Answer: The same as one rotation of 180°
Where you see this in real life
- A Ferris wheel rotates every car about the same centre, which is why nobody's seat gets further from the hub.
- Turning a key rotates it about the centre of the lock — a small angle, but the whole shape moves.
Key words
- Rotate
- turn a shape about a fixed point
- Centre of rotation
- the fixed point the shape turns about
- Clockwise
- the direction the hands of a clock move
- Anticlockwise
- the opposite direction to clock hands
- Congruent
- exactly the same shape and size