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Course 1
12-4 Graphing Reflections
Check 12-3 HW
Course 1
12-4 Graphing Reflections
6th Grade Math HOMEWORK
None
Course 1
12-1 Tables and Functions
Our Learning GoalStudents will
understand functions by creating tables and graphing translations.
Course 1
12-1 Tables and Functions
Students will understand functions by creating tables and graphing translations.
• Learn to use data in a table to write an equation for a function and to use the equation to find a missing value.
• Learn to represent linear functions using ordered pairs and graphs.
• Learn to use translations to change the positions of figures on a coordinate plane.
• Learn to use reflections to change the positions of figures on a coordinate plane.
• Learn to use rotations to change positions of figures on a coordinate plane.
• Learn to visualize and show the results of stretching or shrinking a figure.
Today’s Learning Goal Assignment
Learn to use reflections to change the positions of figures on a coordinate plane.
Course 1
12-4 Graphing Reflections
12-4 Graphing Reflections
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm Up
A parallelogram has vertices (-4, 1), (0, 1), (-3, 4), and (1, 4). What are its vertices after it has been translated 4 units right and 3 units up?
(0, 4), (4, 4), (1, 7), (5, 7)
Course 1
12-4 Graphing Reflections
Problem of the Day
These are rits: 24042, 383, and 4994. These are not rits: 39239, 28, and 5505. Which of these are rits: 39883, 4040, and 101? Why?
101 is a rit because it is the same forward and backward.
Course 1
12-4 Graphing Reflections
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
Additional Example 1: Reflecting Figures on a Coordinate Plane
Give the coordinates of the figure after the given reflection. Reflect parallelogram EFGH across the y-axis.
E F
GH
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12-4 Graphing Reflections
Additional Example 1 Continued
To reflect the parallelogram across the y-axis, write the opposites of the x-coordinates.
The y-coordinates do not change.
EFGH E’F’G’H’
E(–4, 0) E’(4, 0)
F(0, 0) F’(0, 0)
G(–2, –3) G’(2, –3)
H(–6, –3) H’(6, –3)
Course 1
12-4 Graphing Reflections
Additional Example 1 Continued
Reflect parallelogram EFGH across the y-axis.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
xE F
GH
E’F’
G’ H’
Course 1
12-4 Graphing Reflections
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
Try This: Example 1
Give the coordinates of the figure after the given reflection. Reflect parallelogram EFGH across the x-axis.
E F
GH
Course 1
12-4 Graphing Reflections
Try This: Example 1 Continued
To reflect the parallelogram across the x-axis, write the opposites of the y-coordinates.
The x-coordinates do not change.
EFGH E’F’G’H’
E(–4, 0) E’(–4, 0)
F(0, 0) F’(0, 0)
G(–2, –3) G’(–2, 3)
H(–6, –3) H’(–6, 3)
Course 1
12-4 Graphing Reflections
Try This: Example 1 Continued
Reflect parallelogram EFGH across the x-axis.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
xE F
GH
E’ F’
G’H’
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12-4 Graphing Reflections
Additional Example 2: Design Application A designer is using a stencil that is shaped like the figure below. A pattern is made by reflecting the figure across the x-axis. Give the coordinates of the vertices of the figure after the reflection.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
P
QS
R
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12-4 Graphing Reflections
Additional Example 2 Continued
To reflect the quadrilateral across the x-axis, write the opposites of the y-coordinates.
The x-coordinates do not change.
PQRS P’Q’R’S’
P(1, 7) P’(1, –7)
Q(2, 1) Q’(2, –1)
R(–1, 1) R’(–1, –1)
S(–3, 3) S’(–3, –3)
Course 1
12-4 Graphing Reflections
Additional Example 2 Continued
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
P
QS
R
P’
Q’
S’
R’
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12-4 Graphing Reflections
Try This: Example 2
A designer is using a stencil that is shaped like the figure below. A pattern is made by reflecting the figure across the y-axis. Give the coordinates of the vertices of the figure after the reflection.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
P
QS
R
Course 1
12-4 Graphing Reflections
Try This: Example 2 Continued
To reflect the quadrilateral across the y-axis, write the opposites of the x-coordinates.
The y-coordinates do not change.
PQRS P’Q’R’S’
P(–3, 7) P’(3, 7)
Q(–2, 1) Q’(2, 1)
R(–5, 1) R’(5, 1)
S(–7, 3) S’(7, 3)
Course 1
12-4 Graphing Reflections
Try This: Example 2 Continued
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
P
QS
R Q’
P’
S’R’
Course 1
12-4 Graphing Reflections
Lesson Quiz
Give the coordinates of the vertices of each figure after the given reflection.
1. Reflect triangle ABC with vertices A(5, 1), B(2, 3),
and C(4, 6) across the x-axis.
2. Reflect parallelogram PQRS with vertices P(–4, –4),
Q(1, –4), R(–2, 2), and S(3, 2) across the y-axis.
P’(4, –4), Q’(–1, –4), R’(2, 2), and S’(–3, 2)
A’(5, –1), B’(2, –3), C’(4, –6)
Insert Lesson Title Here
Course 1
12-4 Graphing Reflections
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