Transformations, congruence, vectors and similarity Study Guide

Rotation is a type of geometric transformation that moves a figure around a fixed point called the centre of rotation. Unlike reflection or translation, rotation changes the orientation of the figure while maintaining its size and shape. To describe a rotation fully, three key pieces of information are required: the centre of rotation, the angle of rotation, and the direction of rotation. The centre of rotation is the point about which the figure turns; it can be on, inside, or outside the figure itself. The angle of rotation specifies by how many degrees the figure is turned, common angles include 90, 180, and 270 degrees. The direction of rotation can be either clockwise (the same direction as clock hands) or anti-clockwise (the opposite direction). By convention, a positive angle usually denotes an anti-clockwise rotation, while a negative angle denotes a clockwise rotation. When performing a rotation, for each point on the original figure (the object), you measure its distance and angle from the centre of rotation. The corresponding point on the rotated figure (the image) will be at the same distance from the centre and at the new angle specified by the rotation. Tools like tracing paper can be very helpful to visualise and perform rotations accurately, by placing the tracing paper over the figure, marking the centre of rotation, tracing the shape, and then turning the tracing paper around the centre point by the specified angle and direction.

Rotation is a transformation that turns a shape around a fixed point, called the centre of rotation. To fully describe a rotation, you need three pieces of information:

1. Centre of rotation: This is the fixed point around which the shape turns. If not specified, it's often (0,0).
2. Angle of rotation: This is the amount, in degrees, that the shape is turned. Common angles are 90°, 180°, and 270°.
3. Direction of rotation: This is whether the turn is clockwise (the same direction as clock hands) or anti-clockwise (the opposite direction). A 90° clockwise rotation is equivalent to a 270° anti-clockwise rotation. A 180° rotation is the same whether clockwise or anti-clockwise.

When performing a rotation, every point in the shape moves along a circular arc, with the centre of rotation as the centre of the circle. The distance of each point from the centre of rotation remains constant. It's helpful to use tracing paper to visualise and perform rotations accurately. Place the tracing paper over the shape, mark the centre of rotation, trace the shape, then pivot the tracing paper around the centre of rotation by the specified angle and direction. The new position of the traced shape gives the rotated image.