Coordinate Algebra: Unit 5
Name___________________
Date_________________
Lesson 2: Dilations and Translations of Figures
Period________
Guided Notes
Standard and Skills
¨MCC9-12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other points as outputs. Compare
transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
SWBAT represent transformations in the coordinate plane (translations, dilations, reflections, and rotations)
Introductory Vocabulary
Pre-Image: The ________________ figure before undergoing a ___________________.
Image: The ___________, ________________ figure after a _____________________.
Isometry: A transformation in which the pre-image and image are _____________.
Quick Check!
1. Parallelogram MATH is transformed to Parallelogram LOVE by a rotation.
What is the image represents the pre-image of HT?
M
E
A
V
H
T
L
O
2. Find the value of each variable, given that the transformation is an isometry.

6 x
10 72
3y  2
Types of Transformations
Term
Definition
Translations
____________ your pre-image over.
Reflections
____________ your pre-image over.
____________ your pre-image about a
Rotations
fixed point.
____________ or ___________ your preDilation
image.
Quick Check!
1. Identify the transformation pictured for each image.
2. A figure has vertices at X(3, -3), Y(1, -2),
and Z(3, 0). After a transformation, the
image of the figure has vertices at
X’(-3, -3), Y’(-1, -2), and Z’(-3, 0).
Draw the preimage and the image.
Then identify the transformation.
Picture/Example
I. Translations
Rules for Translations
To translate a shape, every point of the shape must move:
1.______________________________________
2. ______________________________________
Adding/ subtracting to the x and y variables generates a ____________________ on the coordinate plane.
Adding to the X variable moves the pre-image ________________.
Subtracting from the X variable moves the pre-image __________________.
Adding to the Y variable moves the pre-image __________________.
Subtracting from the Y variable moves the pre-image______________.
Example 1: Identify what the rule does to the pre-image.
T( x + 1, y - 1) =
T(x -1, y + 1) =
Guided Practice Describe each transformation.
4.
5.
6.
7.
1. T(x+10, y)
2. T(x–5, y)
3. T(x, y+7)
Example 2: Translate ABC 6 units to the right.
A
T(x, y–6)
T(x+3,y–7)
T(x–4,y–5)
T(x–8,y+9)
Example 3: Translate the image ABC by (x – 8, y + 2), given that ABC has the coordinates A(-2, 4), B (0, -8) and
C (-3,5)
Guided Practice:
1. Translate ABC using the rule (x + 4 , y – 5) given that A (-5, 4) B (-2, 3) C (-3, 1)
I. Dilations
A Dilation is the ____________ or ______________ of a shape.
Dilation Notation: Dk (x, y) = (kx, ky)
Example: Dilate the figure ABC by (2x, 2y) given that A (-2,-2) B(1,-1) and C(0, 2). What are the new coordinates?
Independent Practice
1. Translate the image by (-x , y +2)
A  2 ,3  
B  1, 5  
C  4,8  
2. Translate the image by (x – 2 , -y)
G  2,  7  
H  3, 9  
I  6,11 
3. Given ABC: A5,2 , B3,5 , and C2,2 , and the transformation T  x, y  
 x,
– y  , what are
the coordinates of the vertices of T (ABC)?
What kind of transformation is T?
4. Given the transformation of a translation T(x, y) = (x + 5, y – 3), and the points P (–2, 1) and Q (4, 1), show that
the transformation of a translation is isometric by calculating the distances, or lengths, of PQ and P'Q' .
PQ  _______
P'Q'  ______
Dilate each figure using the given rule.
a. (2x, 2y)
b. ( ¼x, ¼y)
c. (3x, 3y)