Rotations

Rotations

Characteristics of a Rotation on a Plane

Rotation is a transformation which rotates all points on a plane about a fixed point known as the centre of rotation through a given angle in a clockwise or anticlockwise direction.

In order to describe a rotation, we give:

• the centre of rotation,
• the angle of rotation, and
• the direction of rotation

Example 1

Copy the figure T and rotate 180° about the origin.

Different Rotation on a Plane by Drawings

When you turn a ruler at its end corner through an angle, it makes a rotation. A rotation is a transformation which moves a point through a given angle about a fixed point.

A rotation is a transformation that turns a figure about a fixed point called a centre of rotation. You can rotate the figure as much as 360 degrees. The transformation of rotation is usually denoted by $R$. The symbol $R_{\theta}$ means that an object is rotated through an angle $\theta$. In the xy-plane, when $\theta$ is measured in the clockwise direction it is negative and when it is measured in the anticlockwise direction it is positive.

P is on the x-axis

After a rotation through 90° about the origin it will be on the y-axis. Since P is 1 from O, P' is also 1 from O, the coordinates of P are $P'(0,1)$. Hence $R_{90^\circ}(1,0) = (0,1)$