In this chapter, we will learn about the concept of rotation in math with examples.

## What is Rotation in Math ?

When a **point or object is moved from one location to another around the central point** then the movement is called Rotation.

The **Rotation has following features**;

(a) Object is moved around central point / axis

(b) Both the initial & final position are equidistant from the central point after rotation.

(c) the angle formed between initial position, final position and the center is called angle of rotation.

(d) When a point is rotated 360 degree around the central point, a circle is formed.

Let us understand above features with the help of a example.

In the above figure, point A is rotated around central point O to reach point B.

The given rotation has following features;

Initial Position ⟹ A

Final Position ⟹ B

Angle of rotation ⟹ 40 degree

Center of rotation ⟹ O

Distance OA = OB

## How to rotate a Point

Given is the point A and you want to rotate it around central point O at 80 degree angle.

Let us find angle measurement of existing points with respect to horizontal line.

The angle measurement of ∠LOA = 60 degree.

To get 80 degree rotation, we need to add 20 degree more to the existing angle.

Remove the line OL, you will get total angle of 80 degree.

Take a divider and set it to length OA.

Place one leg of divider on point O and cut an arc on line OM.

Here we get point B after rotating point A by 80 degree.

Note that the distance OA = OB

I hope you understood the rotation of given point by fixed angle.

## Type of Point Rotation

There are **two types of point rotation**.

(a) Clockwise Rotation

(b) Anticlockwise Rotation

### Clockwise Rotation of Point

When a point is moved clockwise around the central point then the rotation is termed clockwise.

**For example**;

Here the point A is rotated in clockwise direction to position B around the central point O.

### Anti-clockwise rotation of point

When a point is moved anti-clockwise around the central point O, then the movement is called anti-clockwise rotation.

For example;

In the above figure, point A is rotated to point B in anticlockwise direction.