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In Geometry, transformation means changing the appearance of an object. There are many ways in which this can be done viz translation, reflection, rotation etc.

Rotation in math definition

Rotation is a transformation in which a geometric figure is turned around a certain point. Thus in rotation there is a central point that is fixed and the figure moves around that point in a circle. A complete rotation is when the object rotates by 360°.

In rotation, the figure does not change its size or shape. The only change is in the direction.

Terms related to rotation of shape
Let us understand some of the terms that are frequently used along with the rotation function:

Preimage - this term is used to refer to the original object
Image - this term is used to refer to the object after it has been rotated.
Angle of rotation - the amount by which the object is rotated is measured in degrees and is called the angle of rotation.

Properties of a rotation

• In rotation, the distance between any point on the shape and the center of rotation always remains the same.
• The point around which the object is rotated can be a point inside the object itself or a point outside it.
• When the object is rotated in a clockwise direction then the angle of rotation is negative and when the object is rotated in an anti-clockwise direction, the angle of rotation is positive.

Did you know?
When a triangle is rotated about X-axis, it forms a cone with its axis of symmetry as the same X-axis.

Rotating 90° is the same as rotating 270° in the opposite direction.

Practice questions:
Question: Draw the new position of the point A after it has been rotated around the origin (0,0)

Pre-image of point A is as shown in the figure below:

Rotation
1. 90° clockwise rotation
2. 180° clockwise rotation
3. 270° clockwise rotation
4. 360° rotation
5. 90° counter clockwise rotation
6. 270° counter clockwise rotation

Question: Draw the new position of the triangle ABC after it has been rotated around the origin (0,0)

Pre-image of the triangle ABC is as shown in the figure below

Rotation
1. 90° clockwise rotation
2. 180° clockwise rotation
3. 270° clockwise rotation
4. 360° rotation
5. 90° counter clockwise rotation
6. 270° counter clockwise rotation

As you can see, a 360° rotation brings the shape back to its original position.

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