8.7 translations and rotations 1
TRANSCRIPT
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