2.3 Rotation

• Rotation about a point
• Centre of rotation, angle and direction
• Rotation on the Cartesian plane
• Properties of rotation
• Rotational symmetry and order of symmetry

• describe a rotation by its centre, angle and direction
• rotate a figure about a given point
• determine images under rotation of 90, 180 and 270 degrees about the origin
• determine the order of rotational symmetry of a figure
• appreciate rotational symmetry in the environment

“What three things must you know to turn a shape exactly?”

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1. Rotating a figure
   40 min · 2 practice tasks · quiz
   The three things a rotation needs, and the coordinate rules about the origin.
2. Rotational symmetry
   40 min · 2 practice tasks · quiz
   Counting how many times a shape fits onto itself in a full turn.
3. Deriving the 90 degree anticlockwise rule
   40 min · 1 practice tasks · quiz
   A quarter-turn anticlockwise about the origin sends (x, y) to (-y, x). Build it from a plotted point, not from memory.
4. 90 degrees clockwise and 270 anticlockwise
   40 min · 1 practice tasks · quiz
   Clockwise 90 degrees about the origin sends (x, y) to (y, -x), which is the same as 270 anticlockwise.
5. Half-turns of 180 degrees
   40 min · 1 practice tasks · quiz
   A half-turn about the origin negates both coordinates. About any other centre, the centre is the midpoint of each point and its image.
6. Rotation about a point that is not the origin
   40 min · 1 practice tasks · quiz
   Subtract the centre, rotate as if it were the origin, add the centre back.
7. Finding the centre of rotation
   40 min · 1 practice tasks · quiz
   The centre lies on the perpendicular bisector of every segment joining a point to its image.
8. Finding the angle and the direction
   40 min · 1 practice tasks · quiz
   Join the centre to a point and to its image; the angle between those rays is the turn, and the arrow gives clockwise or anticlockwise.
9. Inverse rotations and combining turns
   40 min · 1 practice tasks · quiz
   The inverse turns back through the same angle about the same centre. Two rotations about the same centre add their signed angles.
10. Rotational symmetry in the environment
    40 min · 1 practice tasks · quiz
    Read the order of rotational symmetry in craft, buildings, wheels and logos, and design a motif with a given order.