8.7 translations and rotations 1

Lesson 8.7, For use with pages 439-444

How many lines of symmetry does the letter have?

2.1.

Lesson 8.7, For use with pages 439-444

How many lines of symmetry does the letter have?

ANSWER 2ANSWER 2

2.1.

Translations and Rotations

Section 8.7

P. 439 - 443

Essential Questions

• What are the similarities and differences among transformations?

• How are the principles of transformational geometry used in art, architecture and fashion?

• What are the applications for transformations?

• In this section you will learn how TRANSLATE (slide)

and ROTATE (turn) figures in a coordinate plane.

• A translation is a transformation that moves EACH point of a figure the same distance in the same direction.

• Think of it as “SLIDING” the figure on the coordinate plane.

• The image is congruent to the original figure.

Translation

• Translation:– A change in the x: moves the figure left or right

• Add: moves right Subtraction: moves left

– A change in the y: moves the figure up or down• Add: moves up Subtraction moves down

• A translation may look like this:

(x, y) (x + 6, y – 3)

This means each point is moved 6 units to the right and then 3 units down

• Describe these translations:

• (x , y) (x -4, y + 3)

(x, y) (x , y -2)

Left 4, up 3

Down 2

GUIDED PRACTICE for Example 1

1. Describe the translation from the blue figure to the red figure.

SOLUTION

Each point moves 5 units to the left and 4 units down. The translation is

(x, y) → (x – 5, y – 4) .

1. RST has vertices R(–1, 4), S(3, 4), and T(2, –3). Translate the figure. (x, y) → (x – 2, y + 3).∆

ANSWER

R'(–3, 7), S'(1, 7), T'(0, 0)

EXAMPLE 1 Using Coordinate Notation

Translate the figure.

A (-5,4) B(-2,3)

C(-2,0) D(-5,0)

SOLUTION

Each point moves 6 units to the right and 3 units down. The translation is

(x, y) → (x + 6, y –3)

EXAMPLE 1 Using Coordinate Notation

Translate the blue figure.

A (-5,4) B(-2,3) C(-2,0) D(-5,0)

(x, y) → (x + 6, y –3)

Homework

• Page 442 #4-7, 16AB