Rotation
A rotation turns a shape about a fixed point. To describe one you need
three things:
- a centre — the fixed point the shape turns around;
- an angle — how far it turns, e.g. 90^\circ,
180^\circ or 270^\circ;
- a direction — clockwise or anticlockwise.
The shape keeps its size, its angles and its orientation — a rotation is
not a mirror image. Every point simply stays the same distance from the
centre as it swings around.
Rotating about the origin
When the centre is the origin (0, 0), each turn has a tidy
coordinate rule:
For a point (x, y) rotated about the origin:
- 90^\circ anticlockwise:
(x, y) \to (-y, x);
- 180^\circ:
(x, y) \to (-x, -y);
- 90^\circ clockwise:
(x, y) \to (y, -x).
Seeing it on a grid
Take the triangle with corners (1,1),
(3,1) and (1,2), and rotate it
90^\circ anticlockwise about the origin. Each corner follows
(x, y) \to (-y, x), so it swings a quarter-turn round the marked
centre while keeping its shape.