Silent Do Now
*Take out your weekly sheet & homework
1.
2. Sierra has budgeted $107 a month for entertainment
expenses, such as movies, concerts, and sporting events. By
the end of the second week of July, she had already spent $65
on entertainment expenses. She plans to only go to movies for
her entertainment in the last two weeks of July, and the
theater she goes to charges $7 per ticket. If she wants to stay
at or under budget, and x represents the number of tickets to
the movies she can buy, which of the following inequalities
symbolizes this situation?
A. $7x + $65 < $107
B. $65x + $7 > $107
C. $7x + $65 > $107
D. $65x + $7 < $107
Agenda
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Review Do Now
Pass Back Exit Tickets
Reflections & Rotations
Exit Ticket
Reflections!
Vocabulary
• Reflection: A FLIP over a line.
• Line of Symmetry: The LINE where you could
fold the image and have both halves match
exactly.
Reflection Rules
• To reflect point (a, b) across the Y-AXIS use the opposite of
the x-coordinate and keep the y coordinate the same.
• To reflect point (a, b) across the X-AXIS keep the xcoordinate the same and use the opposite of the ycoordinate.
• To reflect point (a, b) across the X AND Y AXIS use the
opposites of both coordinates.
• To reflect point (a, b) across the line Y=MX + B 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?
Example 2
Reflect figure ABC over the x axis. The original
figure has coordinates A (1,3), B (1,1) and C
(4,1)
• What is the rule?
Guided Practice!
EOCT Question!
What is the rule for a reflection across the y-axis
followed by a translation 9 units to the left
and 2 units down?
A. (x' , y') = (x - 9 , -y - 2)
B. (x' , y') = (-x - 9 , y - 2)
C. (x' , y') = (-x + 9 , y + 2)
D. (x' , y') = (x + 9 , -y + 2)
Rotations!
Exit Ticket on Reflections!
1. Reflect the rectangle ABCD across the x-axis
given that it has coordinates A(-8,-2), B(-2,-2),
C(-2,-9) and D(-8,-9).
2. Write the rule for any figure that is reflected
over the y-axis.
3. What happens if I reflect a figure over the line
y = x?
Rotations
Rotations
turn around a center.
A rotation is a ________
distance from the center to any
The _______________
point on the shape stays the ___________.
same
Degrees of Rotation
Let’s compare Clockwise and Counterclockwise
270°𝐶𝐶𝑊
90CW  _____
____
180CW
 180°𝐶𝐶𝑊
_________
270CW
90°𝐶𝐶𝑊
 _____
____
Degrees of Rotation (Ctd.)
Rotate 90 Clockwise about
the Origin
 x,y    y, x 
Change the sign of x and switch the order
Let’s try some examples!
Rotate 90° clockwise
about the origin
A(7, 3) 
 A'(
B(1, 4) 
 B'(
C(3, 1) 
 C'(
,
,
)
)
,
)
Rotate 90° CW about the origin
Same as 270° CCW
A(7, 3)  A'  3,7 
B(1, 4)  B'  4, 1
C(3, 1)  C' 1, 3 
Rotate 180 about the Origin
 x,y    x, y 
ONLY Change the signs
Rotate 180° about the origin
Q(8,  2) 
 Q'(
,
)
R(8,  9) 
 R'(
,
)
S(2,  2) 
 S'(
,
)
T(2,  9) 
 T '(
,
)
Rotate 180° about the origin
Q(8,  2)  Q'  8,2 
R(8,  9)  R'  8,9 
S(2,  2)  S'  2,2 
T(2,  9)  T '  2,9 
Rotate 270 CW about the Origin
Same as 90 CCW
 x,y    y,x 
Change the sign of y and switch the order
Rotate 90° CCW
about the origin
E(3,  2) 
(
,
)
F(6, 5) 
(
,
)
G(0, 2) 
(
,
)
Rotate 90° CCW
about the origin
E(3,  2)  E'  2, 3 
F(6, 5)  F'  5, 6 
G(0, 2)  G'  2,0 
Independent Practice!
You try!
Rotate 270 Counterclockwise about the Origin:

 
90°𝐶𝑊Rule : _______________
x,y  y, x
Same as _________

Exit Ticket
1. Rotate a figure ABC located at A(2,2) B (8,2)
and C(6,8) 180 degrees clockwise. What
would be the coordinates of the new figure?
2. (X, Y) -> (-Y, X) represents which type of
rotation? How do you know?