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Course 1
12-4 Graphing Reflections
Check 12-3 HW
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Course 1
12-4 Graphing Reflections
6th Grade Math HOMEWORK
None
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Course 1
12-1 Tables and Functions
Our Learning GoalStudents will
understand functions by creating tables and graphing translations.
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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.
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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
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12-4 Graphing Reflections
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
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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
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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
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-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
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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)
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12-4 Graphing Reflections
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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
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-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
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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
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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’
Course 1
12-4 Graphing Reflections
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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
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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)
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12-4 Graphing Reflections
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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
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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
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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)
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12-4 Graphing Reflections
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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’
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12-4 Graphing Reflections
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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