Reflection, rotation and rotational symmetry
Plot points in all four quadrants, reflect shapes in an axis, rotate them about a point, and find shapes with a centre of symmetry.
- UK: Year 5
- France: grade 7
- Germany: grade 6
- Iran: grade 5
- Afghanistan: grade 8
- Syria: grade 5
- Palestine: grade 7
- Ukraine: grade 6
- Russia: grade 6
Guide
Extending both axes past 0 splits the grid into four quadrants. A negative x-coordinate is left of the origin; a negative y-coordinate is below it. (−3, 2) means 3 left, then 2 up.
A reflection works like a mirror: every point ends up the same distance away on the other side of the mirror line. Reflecting in the y-axis changes the sign of x and keeps y. The classic slip is sliding the shape across instead of flipping it.
In a rotation the shape turns about a point, the centre of rotation. For 90°, turn the line from the centre to each vertex through a quarter turn. Tracing paper with a pencil point on the centre helps a lot. (Rotation is not in the KS2 curriculum; treat it as enrichment.)
A shape that fits onto itself after a half turn has rotational symmetry of order 2 (also called point symmetry), and the point it turns about is its centre of symmetry: parallelograms and rectangles are examples. An equilateral triangle fits onto itself after a third of a turn (order 3), but not after a half turn.