Rotations and symmetry

Rotating points by 90°, 180° and 270° about the origin, line symmetry and rotational symmetry of shapes.

Rotations about the origin

Rotating a point about the origin

Drag P and check the rules. Try sketching each image on paper.

Example 1●●

Rotate $(2, 5)$ by $90^\circ$ anticlockwise about the origin.

$(x, y) \to (-y, x)$ gives $(-5, 2)$.

Symmetry

A shape has line symmetry if a mirror line folds it onto itself. Its order of rotational symmetry is the number of times it fits onto itself in one full turn.

Example 2●

Find the lines of symmetry and order of rotational symmetry of a square.

$4$ lines of symmetry, order $4$.

Flashcards

Rotate $180^circ$

$(x, y) \to (-x, -y)$

Rectangle

$2$ lines, order $2$

Regular hexagon

$6$ lines, order $6$

Practice

Rotate $(2, 5)$ by $90^\circ$ anticlockwise about the origin.
Rotate $(2, 5)$ by $180^\circ$ about the origin.
Rotate $(3, 1)$ by $90^\circ$ clockwise about the origin.
Order of rotational symmetry of a square?
Lines of symmetry of an equilateral triangle?
Order of rotational symmetry of a rectangle (not a square)?
Lines of symmetry of an isosceles triangle (not equilateral)?
Lines of symmetry of a parallelogram (not a rectangle or rhombus)?