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12-4 Graphing Reflections

Check 12-3 HW

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12-4 Graphing Reflections

6th Grade Math HOMEWORK

None

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12-1 Tables and Functions

Our Learning GoalStudents will

understand functions by creating tables and graphing translations.

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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.

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12-4 Graphing Reflections

12-4 Graphing Reflections

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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)

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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.

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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)

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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’

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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

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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)

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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)

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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

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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)

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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’

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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

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12-4 Graphing Reflections