A figure is said to have a point symmetry about its centre O, if for every point P on the figure, there is another point Q directly opposite to it on the other side of O at the line OP such that OP = OQ.
While rotating an object about a fixed point through an angle of 3600, if it repeats itself more than one time, the object is said to have a rotational symmetry.
In a complete turn of 360°, the number of times an object looks exactly the same is called the order of rotational symmetry. If an object matches its original appearance only once in a full 360° rotation then the object does not have rotational symmetry and the order of symmetry is 1.
The smallest angle by which an object is rotated so that it repeats its original form is known as angle of rotational symmetry.
If a point P(x, y) is rotated through 900 clockwise about the origin to the point Q, then the coordinates of Q are (y, –x).
If a point P(x, y) is rotated through 900 anticlockwise about the origin to the point Q', then the coordinates of Q' are (–y, x).
If a point P(x, y) is rotated through 1800 about the origin to the point Q, then the coordinates of Q are (–x, –y).
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