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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