Transformations

December 2, 2009

Objectives

What is a transformation?

• A transformation is a change in position, shape, or size of a figure.

• There are four basic transformation that you will investigate in this chapter.

• Each transformed figure is the image of the original figure. The original figure is called the preimage.

Four types of transformations

What is an isometry?

• An isometry is a transformation in which the original figure and its image are congruent.

• Which are isometries?– Flips– Slides– Turns– Changes size

Notation• A transformation maps a

figure onto its image.• We often use an arrow (→)

to indicate a mapping. Prime notation is sometimes used to identify image points.

• In the diagram, Z' (read "Z prime") is the image of Z. Notice that the corresponding points of the original figure and its image are listed in the same order.

Practice

a. Name the image of A.b. Name the preimage of

B'.c. Which of the four types

of transformations shown at the beginning of this section is illustrated in the figure above?

Reflections = Flips

• A flip is also known as a reflection. • Reflections have many properties which are

listed below.– A reflection reverses orientation.– A reflection is an isometry.

More about reflections• Other properties of a

reflection form the basis of its definition. A reflection in line r is a transformation for which the following are true.

• If a point A is on line r, then the image of A is itself.

• If a point B is not on line r, then r is the perpendicular bisector of BB'

Creating a reflection

• Reflecting across a line

Creating a reflection on a coordinate plane

• Reflect across the x axis

Creating a reflection on a coordinate plane

• Reflect across the y axis

Creating a reflection on a coordinate plane

• Reflect across the y=2

Creating a reflection on a coordinate plane

• Reflect across the x= -2

Creating a reflection on a coordinate plane

• Reflect across the y=x