1. Getting Started… 9.6 - Translations
Find y (figure not drawn to scale!):
139º
5yº
71º
9yº
92º
Y = 17

2. The action of sliding a figure in any direction.
Translation (Slide)
The action of sliding a figure in any direction.

3. Translation
The act of sliding a figure in any direction.

4. Reflection (flip - mirror)
The result of a figure flipped over a line.

5. Reflection
The result of a figure flipped over a line.

6. The action of turning a figure around a point or a vertex.
Rotation (Turn)
The action of turning a figure around a point or a vertex.

7. Turning a figure around a point or a vertex
Rotation

8. Terminology B B’ Horizontal Translation A A’
Image – final image after transformation
Labeled with “Prime”
Pre-image – image before transformation
Labeled with Capital Letters B B’
Horizontal Translation A A’
Pre-Image
Image

9. Translation A
Image
Pre-Image
Slide Arrow C B A’ B’ C’

10. Algebraic Translations
Let B have coordinates (2,5). Find the image of B after the following translation:
Left 4 units , up 2 units:
Right 5 units, down 9 units:
(-2, 7)
(7, -4)

11. Try some more!
Let point C have the coordinates (-4,1). Find the image coordinates C for each translation.
- (x,y)  (x + 3, y – 1)
-(x,y)  (x – 2, y + 5)
(-1, 0)
(-6, 6)

12. Find the image coordinates for each translation(x, y) → (x-5, y)4 3 2 1 -5 -4 -3 -2 -1 B B A C C A

13. Find the image coordinates for each translation5 4 3 2 1 -5 -4 -3 -2 -1
Find the image coordinates for each translation
(x, y) → (x-1, y + 3) B A D C B A C D

14. Triangle ABC has vertices A(–2, 1), B(2, 4), and C(1, 1).
Find the coordinates of the vertices of the image if it is translated 3 units to the right and 5 units down.
Answer: The coordinates of the vertices of the image are A(1, –4), B(5, –1), and C(4, –4).
Example 2-3a

15. Graph triangle ABC and its image.
Answer: B
The preimage is .
A(–2, 1), B(2, 4), and C(1, 1). A C B
The translated image is A(1, -4), B(5, -1), and C(-4, -4). A C
Example 2-3b

16. Triangle JKL has vertices J(2, –3), K(4, 0), and L(6, –3).
a. Find the coordinates of the vertices of the image if it is translated 5 units to the left and 2 units up.
b. Graph triangle JKL and its image.
Answer: J(–3, –1), K(–1, 2), L(1, –1)
Answer:
Example 2-3c

17. Last One  What is the equation of this line? Name an equation of
a line that is
translated vertically
3 units up?

19. Homework Extra Practice 9.6