ROTATION AND ROTATIONAL SYMMETRY

The point about which the hands of the clock, or the spokes of the wheel rotate, is called the centre of rotation.

The angle through which the hands or the spokes turn is called the angle of rotation.

The globe of the world rotates about a line called the axis of rotation.

During a rotation, the distance of any point from the centre of rotation does not change.

A rotation is the turning of a shape or figure about a point and through a given angle.

90 degree rotation :

90-degree-rotation

The figure is rotated counter clockwise about O through 90 degree.

180 degree rotation :

180-degree-rotation

The figure is rotated counterclockwise about O through 180 degree.

Problem 1 :

Consider the rotations of 

center-of-rotation-q1

which follow

center-of-rotation-q1p1

Which of A, B, C and D is a rotation of the object through :

a) 180    b) 360    c) 90   d) 270

Solution :

Figure A :

Counter clockwise 90 degree rotation.

Figure B :

Counter clockwise 180 degree rotation.

Figure C :

Three times counter clockwise direction 90 degree. Which is equal to 270 degree counter clockwise direction.

Figure D :

360 degree counter clockwise rotation.

Copy and rotate each of the following shapes about the centre of rotation O, for the number of degrees shown. You could use tracing paper to help you.

Problem 2 :

rotation-and-rotational-symmetryq1

Solution :

Rotating the given figure with 90 degree counter clockwise direction, we get

rotation-and-rotational-symmetryq1s.png

Problem 3 :

rotation-and-rotational-symmetryq2.png

Solution :

Rotating the given figure with 180 degree counter clockwise direction, we get

rotation-and-rotational-symmetryq2s.png

Problem 4 :

rotation-and-rotational-symmetryq3.png

Solution :

Rotating the given figure with 270 degree counter clockwise direction, we get

rotation-and-rotational-symmetryq3s.png

Problem 5 :

rotation-and-rotational-symmetryq4.png

Solution :

Rotating the given figure with 360 degree counter clockwise direction, we get

rotation-and-rotational-symmetryq4s.png

Problem 6 :

rotation-and-rotational-symmetryq5.png

Solution :

Rotating the given figure with 90 degree counter clockwise direction, we get

rotation-and-rotational-symmetryq5s.png

Problem 7 :

rotation-and-rotational-symmetryq6.png

Solution :

Rotating the given figure with 270 degree counter clockwise direction, we get

rotation-and-rotational-symmetryq6s.png

Problem 8 :

rotation-and-rotational-symmetryq7.png

Solution :

Rotating the given figure with 180 degree counter clockwise direction, we get

rotation-and-rotational-symmetryq7s.png

Problem 9 :

rotation-and-rotational-symmetryq8.png

Solution :

Rotating the given figure with 90 degree counter clockwise direction, we get

rotation-and-rotational-symmetryq8s.png

Problem 10 :

rotation-and-rotational-symmetryq9.png

Solution :

Rotating the given figure with 90 degree counter clockwise direction, we get

Problem 11 :

rotation-and-rotational-symmetryq9s.png

Solution :

Rotating the given figure with 90 degree counter clockwise direction, we get

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