Transformations

By Lisa Budi Rahayu, SSi

Rotation• Rotation occurs when an object is turned

around a given point• Rotation can be clockwise or anti-clockwise• The fixed point is called the centre of rotation • the angle through which the shape is rotated

is called the angle of rotation

Properties of rotation• Anti-clockwise rotation is positive and clockwise

rotation is negative• A rotation through 1800 is a half turn, a rotation

through 900 is a quarter turn • A point and its image are equidistant from the

centre of rotation• Each point of an object moves along the arc of a

circle whose centre is the centre of rotation• Only the centre of rotation is invariant• The object and the image are directly congruent

Properties of rotation• The perpendicular bisector of a line joining a

point and its image passes through the centre of rotation

• A line segment and its image are equal in length

• Exercise on Cambridge Book• Page : 252

Assessment

Enlargement• Enlargement is a transformation in which each

point of an object is mapped along a straight line drawn from a fixed point

• The fixed point is called the centre of enlargement

• The distance each point moves is a certain number multiplied by its distance from the center of enlargement

• SF = image length_ original length

Properties of enlargement• The centre of enlargement can be anywhere• A scale factor greater than 1 enlarges the object

whilst a scale factor smaller than 1 reduce the object

Properties of enlargement• If a point and its image are on opposite sides of

the centre of enlargement, then the scale factor is negative

• An object and its image are similar with sides in the ratio 1 : k; where k is the scale factor

• The areas of the object and its image are in the ratio 1 : K2

• Angles and orientation of the object are invariant

• Exercise on Cambridge Book• Page : 254

Assessment