Chapter 9: Transformation and Congruency

Quadrant Review

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

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

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.

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’

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

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)

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)

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)

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>

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