1. Chapter 9: Transformation and Congruency

2. Quadrant Review

3. Integer Review Adding integers: SAME SIGN= add and keep the sign
DIFFERENT SIGN: subtract and take the sign of the higher absolute value
Subtract integer:
ADD the OPPOSITE
Multiply and Divide:
Same sign positive
Different sign negative
Practice worksheet

4. Vocabulary
Transformation: a function that describes a change in the position, size, or shape of a figure
Preimage: The input of a transformation- the original
Image: the output of the transformation- the end result after the transformation. The vertices are labeled using prime notation ‘
Translation transformation that slides a figure along a straight line
Orientation: the way a figure is presented
Congruent: same size, same shape

5. Partner Work Explore Activity pg.279 Move 7 units to the right and
5 units down
The original points are=
A= (1,11) B= (3, 7) C= (1, 7)
A’B’C’ =(x +7, y -5)
A’= (8,6) B’= (10, 2) C= (8, 2)
1. the orientation is the same. It is not affected by the translation.

6. Explore Activity page 280
Corresponding sides: matching sides in a similar figure.
E:The image and preimage have corresponding sides are congruent.
Parallel: two lines sides by sides that continue to have the same distance between them.
I: TR //PA, T’R’ //P’A’

7. Pg. 280 2. Conjecture about the translation:
The figure has the same size, shape and orientation
3. The image and preimage in a translation are congruent

8. Graphing Translations
The figure shows a triangle XYZ. Graph the image of the triangle after the translation of 4 units to the right and 1 unit up. (x+4, y+1)
Step 1: translate each point
If you move a units to the right (x, y) --- (x+a, y)
If you move a units to the left (x, y)--- (x-a, y)
If you move b units up (x,y)--- (x, y +b)
If you move b units down (x,y)--- (x, y-b)

9. Graphing Translations
Step 1:
x= (-4, 1) move right 4 units and up 1 unit
(-4 +4, 1 +1) = x’=(0,2)
Y= (0, -1)
(0 +4, -1 +1) = y’=(4,0)
Z= (-2, -3)
(-2 +4, -3 +1) = z’=(2,-2)

10. Page 282 #4 Tell me the coordinates for the preimage
Tell me the translation function
Tell me the coordinates for the image
A(0,3) B(3,3) C(5,-1) D(2,-1)
<x-5, y-2>
A’ (0-5, 3-2) = A’(-5,1)
B’ (3-5, 3-2) = B’(-2,1)
C’ (5-5, -1-2) = C’(0,-3)
D’ (2-5, -1-2) = D’(-3,-3)

11. Using algebraic rules to describe translations
How would you find the rule?
Step 1: Find the preimage
X (-4,1) Y (0, -1) Z (-2, -3)
Step 2: Find the image
X (0,2) Y (4,0) Z(2, -2)
Step 3: Find the difference
The figure went right 4 units and up 1)
<x+4, y +1>

12. Activity  Cut out you pentagon and grab a paper clip.
Let’s use this model to practice translations