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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
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