Math 7 - Unit 6: Geometry
Sec. 6.1 Translations and Reflections (SOL 7.8)
Name____________________________
Date_____________________________
WHAT ARE TRANSFORMATIONS ?
Transformations are methods used to MOVE or CHANGE figures plotted over a coordinate plane.
TRANSLATION : _________________________________________________
______________________________________________________________________
FOLLOW coordinate point format:
(x , y )
This first number represents:
This second number represents:
Example:
Translate the object ( –4, 3) .
This means: move each point of the figure like this:
Figure
Vertex
A
B
D
C
4 units ________ and 3 units ________.
Image
Vertex
Math Work
(x, y )
( x + –4 ,
A (–2, 1)
( –2 + –4
B (3, 1)
( x’ , y’ )
y+3 )
, 1+3 )
=
A’ ( – 6 , 4 )
(
)
=
B’ (
)
C(
)
(
)
=
C’ (
)
D(
)
(
)
=
D’ (
)
Practice 1: Translate the object (– 5, 6)
Figure
Coordinates
Image
Coordinates
Math Work
A
A’
B
B’
C
C’
A
B
C
Practice 2: Translate the object (10, –6 ). Label the figure and image vertex in the table.
H
Figure
Coordinates
Math Work
Image
Coordinates
K
G
M
REFLECTION: __________________________________________________
__________________________________________________________________
Let’s get an idea:
Reflect this object
Reflect this object
over the x –axis :
over the y–axis:
Reflect this object
Reflect this object
over the y –axis :
over the x–axis:
Reflection over x – axis:


x-coordinate stays the same
y-coordinate becomes opposite sign
(multiply y-coordinate by -1)
Ex.
(x, y)
→
(x, -y)
(3, 1)
→
(3, -1)
(6, 1)
→
(
)
(3, 6)
→
(
)
(6, 6)
→
(
)
Reflection over y – axis:


y
x-coordinate becomes opposite sign
(multiply x-coordinate by -1)
y-coordinate stays the same
Ex.
(x, y)
→
B
C
(-x, y)
x
(-2, -3)
→
(2, -3)
(-3, 2)
→
(
)
(0, 1)
→
(
)
A
Practice 3: ∆ CAT has vertices C (-5, 0), A (-5, 4), and T (-2, 4). Graph ∆ CAT and its translation (6, 1).
Then write the new vertices for the new image.
Figure ∆ CAT
Image ∆ C’A’T’
Practice 4:
Rectangle ABCD has vertices A (1, 1), B (1, 5), C (5,5)and D(5, 1). Graph the rectangle and its
translation (2, 1). Then write the new vertices for both.
Figure ABCD
Practice 5:
Rectangle MATH has vertices M (-6, 2), A (-6, -3), T (-4,2)and H(-4, -3). Graph the rectangle
and its translation (4, -2). Then write the new vertices for both.
Figure MATH
Practice 6:
Image A’B’C’D’
Image M’A’T’H’
∆DOG has vertices D (0, 3), O (3, 0), G (4, 2). Graph ∆DOG and its reflection over the y axis
and over the x axis. Then write the new vertices of the two new images.
Vertices of Image reflected over y-axis
_____________________________________
_____________________________________
_____________________________________
Vertices of Image reflected over x-axis
_____________________________________
_____________________________________
_____________________________________
Practice 7:
∆EFG has vertices E (1, 1), F (4, 1), G (1, 3). Graph ∆EFG and its reflection over the y axis and
over the x axis. Then write the new vertices of the two new images.
Vertices of Image reflected over y-axis
_____________________________________
_____________________________________
_____________________________________
Vertices of Image reflected over x-axis
_____________________________________
_____________________________________
_____________________________________
8. Reflect the figure below
across the x–axis.
10. Reflect the figure below
across the x–axis.
9. Draw the figure whose vertices are given
and then reflect it across the y–axis.
11. How was this object reflected?
Math 7 - Unit 6: Geometry
Sec. 6.1 Translations and Reflections (SOL 7.8)
Name____________________________
HOMEWORK
Graph the image of each figure below following the indicated transformation.
1. Translate
(2, 5)
2. Translate
(–3, 4 )
3. Translate
(4, –2 )
4. Translate
(–3 , –5 )
5. Reflect
across the
y–axis
6. Reflect
across the
x–axis
7. Reflect
across the
x–axis
8. Reflect
across the
y–axis