Rotation in Math

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.

What is rotation in math

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.

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