Lesson 12 1 Transformations pp 500 504 Objectives

Lesson 12. 1 Transformations pp. 500 -504

Objectives: 1. To define and illustrate geometric transformations. 2. To define and perform reflections.

In mathematics, the term transformation describes a change in the appearance of points in a plane. It is therefore a correspondence between point locations before and after the change. The figure before transformation is called the preimage while the resulting figure is called the image.

A transformation can be thought of as a movement of figures. Some movements change the size and shape of a figure while other transformations do not.

B A B C A C

Definition A transformation is a one-to-one function from the plane onto the plane.

The transformation called a reflection is similar to a mirror image. Line l is called the line of reflection, or the mirror.

In a reflection, X X (X is mapped to X ), Y Y , and Z Z. If the vertices of the preimage are named in counterclockwise order, XYZ, then the image has clockwise order X Y Z. The order of vertices is called orientation. Reversing the orientation is a characteristic of a reflection.

Y Y Z Z X X l

Definition A reflection in a line, l, is a transformation that maps each point A of a plane onto the point A , such that the following conditions are met. 1. If A is on l, then A = A. 2. If A is not on l, then l is the perpendicular bisector of AA.

Find the image of the segment reflected in the given line. A B B A l

Find the image of the segment reflected in the given line. A A=B l B B=A

Find the image of the segment reflected in the given line. A B l A B

Draw the line of reflection that maps preimage ABC to image A′B′C′. A A C B

Draw the line of reflection that maps preimage ABC to image A′B′C′. A B A C B C

Draw the line of reflection that maps preimage ABC to image A′B′C′. A=C B=B C=A

Homework pp. 492 -493

►B. Exercises 15. Explain how you can find the line of reflection if you are given the preimage and the image of a geometric figure.

►C. Exercises 16. Given: A′B′ is a reflection of AB in l AProve: AB A′B′ B Q A P B l

■ Cumulative Review 18. Name the Platonic solids.

■ Cumulative Review Give the surface area and volume formulas for each figure. Figure 19. Sphere 20. Cylinder 21. Cone 22. Prism with reg. n-gon as a base Surface Area Volume