Acc. Coordinate Algebra: Unit 5
Ms. Matrone
Name___________________
Date_________________
Lesson 1: Introduction Transformations, Translations and Reflections
Period________
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.
( x + 1, y - 1) =
(x -1, y + 1) =
Guided Practice Describe each transformation.
1. (x+10, y)
2. (x–5, y)
3. (x, y+7)
4.
5.
6.
7.
(x, y–6)
(x+3,y–7)
(x–4,y–5)
(x–8,y+9)
Example 2: Identify the rule for a translation of the figure below 6 units right and 3 units down.
A
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)
Practice
1. Translate ABC using the rule (x + 4 , y – 5) given that A (-5, 4) B (-2, 3) C (-3, 1)
2. Translate the image by (x, y +2)
A  2 ,3  
B  1, 5  
C  4,8  
3. Translate the image by (x – 2, y)
G  2,  7  
H  3, 9  
I  6,11 
4. 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?
5. 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'  ______
II. Reflections
Vocabulary
Reflection: A _______________over a line.
Line of Symmetry: The ______________ where you could fold the image and have both halves match exactly.
Reflections Rules
To reflect point (a, b) across the __________________use the opposite of the x-coordinate and keep the y coordinate
the same.
To reflect point (a, b) across the __________________ keep the x-coordinate the same and use the opposite of the ycoordinate.
To reflect point (a, b) across the ___________________________use the opposites of both coordinates.
To reflect point (a, b) across the line __________________ switch the x an y coordinates.
Quick Check!
1. (-x, y) is a reflection over the _______________ axis
2. (x, -y) is a reflection over the _______________ axis.
3. (-x, -y) is a reflection over _____________________.
4. (y , x) represents a reflection over ____________________.
Example 1: Reflect figure ABC using the rule (-x, y). The original figure has coordinates A (1,3), B (1,1) and C (4,1)
What type of reflection is this?
Practice
1. Reflect the figure below three times.
A (-5, 4)
B (-2, 3)
C (-3, 1)
Over the X-Axis
Over the Y-Axis
Over both the X and Y Axis
Reflect each shape over the given line.
1. y – axis
8. x = -1
2. x – axis
9. y = -x
3. y = x
B
C