Rotation

Rotation

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Rotation is a circular movement that has a central point that stays fixed and everything else moves around that point in a circle. A full rotation is 360°. The fixed point about which an object is rotated is called the centre of rotation and the angle through which every point of the object is rotated is called the angle of rotation.
The angle of rotation is positive is the rotation is made in an anti-clockwise direction and it is negative if the rotation is made in a clockwise direction.

Rotation using Co-ordinates

  • Rotation through 90° in an anti-clockwise direction about the centre at the origin(Positive Quater Turn): When we rotate the point along the 90°, the x-coordinate and y-coordinate changes the place and the signs are changed.
    We write this as,
    P(x, y) → P'(−y, x)

  • Rotation through 90° in a clockwise direction about the centre at the origin (Negative Quarter Turn): When we rotate the point along the 90° the y-axis, then y-coordinates remain the same, but x-coordinator are transformed into its opposite.
    We can write it as,
    P(x, y) → P'(y,−x)

  • Rotation through 180° about the centre at the origin (Half Turn): If the image is obtained by the rotation through 180° in an anti-clockwise direction about the centre at the origin is same or the image obtained by the rotation through 180° in clockwise direction.
    We can write it as,
    P(x, y) → P'(−x,−y)

  • Rotation through 90° in an anti-clockwise direction about the centre at the origin (Positive Quater Turn) = P(x, y) → P'(−y, x)
  • Rotation through 90 in a clockwise direction about the centre at the origin (Negative Quarter Turn) = P(x, y) → P'(y, −x)
  • Rotation through 180° about the centre at the origin (Half Turn) = P(x, y) → P'(−x, −y)
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