Reflections Notation
Reflection:

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________
(
/
)
Types of reflections:
Across the x-axis
Across the y-axis
Across the line y = x
Across the origin
Across the line y = -x
Reflection Rules:
𝑟𝑥−𝑎𝑥𝑖𝑠 (
,
)(
,
)
____________________________________
𝑟𝑦−𝑎𝑥𝑖𝑠 (
,
)(
,
)
____________________________________
(
,
)(
,
)
____________________________________
𝑟𝑦= −𝑥 (
,
)(
,
)
____________________________________
𝑟𝑦=𝑥
& __________________________________
𝑟𝑜𝑟𝑖𝑔𝑖𝑛 (
,
)(
,
)
____________________________________
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Example 1:
Reflect the following figure across the x-axis
A=(
, )
A’ = (
,
)
D=(
, )
D’ = (
,
)
M=(
, )
M’ = (
, )
W=(
, )
W’ = (
, )
Rule:
𝑟𝑥−𝑎𝑥𝑖𝑠 (
,
)(
,
)
,
)
Example 2:
Reflect the following figure across the line y = -x
S=(
, )
S’ = (
, )
A=(
, )
A’ = (
,
)
T’ = (
, )
, )
J’ = (
, )
T=( ,
J=(
Rule:
𝑟𝑦= −𝑥 (
,
)
)(
Example 3:
Reflect the following figure across the line y-axis
W=(
, )
W’ = (
, )
I=(
, )
I’ = (
L=(
, )
L’ = (
, )
B=(
,
B’ = (
, )
Rule:
𝑟𝑦−𝑎𝑥𝑖𝑠 (
)
,
,
)
)(
,
)
81
Example 4:
Reflect the figure across y = 1
Example 5:
Reflect the figure across x = -3
Write the rule to describe the transformation
Example 6:
Example 7:
Example 8:
Example 9:
Example 11:
Example 10:
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Reflections
1. ABC has vertices 𝐴(−3,5), 𝐵(−2, −1), and 𝐶(0,3).
Graph 𝑅𝑦=−𝑥 (∆𝐴𝐵𝐶) and label it.
2. When you play pool, you can use the fact that the ball bounces off the side of the pool table at the same
angle at which it hits the side. Suppose you want to put the ball at point B into the pocket at point P by
̅̅̅̅. Off what point on 𝑅𝑆
̅̅̅̅ should the ball bounce? Draw a diagram and explain your
bouncing it off side 𝑅𝑆
reasoning.
3. Given points J(3, 5), A(6, 6), and R(5, 2), graph JAR and 𝑅𝑥=−1 (∆𝐽𝐴𝑅).
3. Graph 𝑅𝑥=0 (∆𝐴𝐵𝐶)
83
Rotation Rules for a Cartesian Coordinate Plane:
𝑅(𝑜,90°) (
,
)(
,
)
____________________________________
& __________________________________
𝑅(𝑜,180°) (
,
)(
,
)
____________________________________
𝑅(𝑜,270°) (
,
)(
,
)
____________________________________
& __________________________________
Example:
Rotate the image 90° clockwise about the origin.
Rule: 𝑅(𝑜,90°) (
,
)(
,
Y=(
, )
Y’ = (
,
)
K=(
, )
K’ = (
,
)
B= (
,
)
B’ = (
, )
U=(
, )
U’ = (
,
)
)
84
Example:
Rotate the image 180° about the origin.
Rule: 𝑅(𝑜,180°) (
,
)(
,
P=(
, )
P’ = (
, )
K=(
, )
K’ = (
,
)
Q= (
, )
Q’ = (
,
)
T=(
, )
T’ = (
, )
)
Example:
Rotate the image 270° clockwise about the origin.
Rule: 𝑅(𝑜,270°) (
Describe the following transformations.
Example 4:
Example 5:
,
)(
,
B=(
,
)
B’ = (
, )
X=(
, )
X’ = (
,
)
N= (
, )
N’ = (
,
)
)
Example 6:
85
Rotate the image in Quadrant III 90° clockwise
Rotate the image in Quadrant III 180° clockwise
Rotate the image in Quadrant III 270° clockwise
86
Name: __________________________ Date: ________________ Hour: _________
Geometry Transformations Test Review
Use the diagram to find the coordinates of the given point.
Part A. A’, the reflection image of A across y = x.
Part B. A’’, the reflection image of A’ across
y = -x.
Part C. A’’’, the reflection image of A’’ across
y = x.
Part D. A’’’’, the reflection image of A’’’ across
y = -x.
Part E. How are A and A’’’’ related?
A is th reflection image of A’’’.
A and A’’’’ have the same x-coordnate, but a different y-coordinate.
A and A’’’’ are the same point.
There is no relation.
A.
B.
C.
D.
2. Rotate A -90⁰; Rotate B 270⁰
3. Use the vector to translate:
4. Translate  x+3,y-2 
A
D
B
________5. Translate point D across
Mapping HS
A B
C
D
F
G
H
I
K
L
M
P
Q
R
S
U
V
X
Y
6. Reflect the figure across x=1
M
I
D
N
E
J
N O
T
Z
87
7. Reflect the figure across line
8. Draw the line of reflection
l
l
9. Reflect the figure across the y axis.
10. Give the coordinates of Point D when
a.) Reflected across x-axis:
b.) Reflected across x= -2:
O
D
B
Y
11. Rotate the figure 45°
12. Rotate the figure 120°
13. Give the angle of rotation from the
dashed figure to the bolded image:
O
O
O
88
14. Rotate AB 270° about point O.
15. Rotate AB 180° about point O
A
O
O
A
B
B
Perform the indicated rotation according to the degrees given using patty paper or a protractor.
16. 180° about point P
17. 270° about point Q
P
Q
Find the mapped point from the given point and What is the angle for each jump?________
angle of rotation about point O.
18. Point B rotated 240° is point ________
A
F
19. Point E rotated 120° is point _________
20. CD rotated 60° is _______________
E
B
O
21. FOA rotated 300° is _____________
22. DE rotated –60° is ______________
23. What is the prime symbol and where is it used?
D
C
24. What is the difference between the image and the pre-image?
25. List and briefly describe the four types of transformations:
89
26. Write the coordinates of the vertices after a rotation
180 counterclockwise around the origin.
D’ 
E’ 
F’ 
G’ 
27. Graph the image of TUV after a translation 10 units left.
28. Which of the following transformations carry
this regular polygon onto itself?
A. Reflection across 𝑙
B. Rotation of 90° clockwise
C. Rotation of 120 counterclockwise
D. Rotation of 40 counterclockwise
90
29. Which of the following transformations carry this regular polygon
onto itself?
A. Rotation of 60 clockwise
B. Rotation of 72° clockwise
C. Rotation of 72 counterclockwise
D. Rotation of 40 counterclockwise
30. Which of the following transformations carry this regular polygon
onto itself?
A. Rotation of 90 counterclockwise
B. Reflection across 𝑙
C. Rotation of 60 counterclockwise
D. Rotation of 72 counterclockwise
31. Look at this diagram:
Which diagram shows EFG rotated 120 counterclockwise about G?
A.
C.
B.
D.
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