Translations

Lesson 9-8

Translations

Translations are used on the coordinate plane.

A translation is a shift or movement of a figure a given number of places on the coordinate plane.

A B

C D

Suppose we have parallelogramABCD as shown on the graph.We can “translate” this shape5 units to the right and 3 unitsdown. The new image wouldlook like this:

EXAMPLE

A B

C D

A’ B’

C’ D’

Notice that the entire new imageIs shifted 5 units to the right and3 units down. The labels of the image are noted with a prime ‘ symbol.

TRY THIS

Q

R

S

Translate triangle QRS 4 units toThe left and 5 units up.

TRY THIS

Q

R

S

Translate triangle QRS 4 units toThe left and 5 units up.

Q’

R’

S’

Symmetry and Reflections

Lesson 9-9

Reflection is a mirror image of a figure.

In geometry, reflectional symmetry occurs when one half of a figure is a mirror image of the other half.

The line of symmetry is the line that divides a figure into two congruent halves.

Symmetry Notice that one half of the

pentagon is the mirror image of the other.

Line of symmetry

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Which of the following figures have reflectional symmetry?

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Which of the following figures have reflectional symmetry?

YES NO

YES YES

YES

Symmetry

Many figures have more than one line of symmetry. Notice that the square has 4 lines of symmetry.

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Draw all the lines of symmetry for the following figures.

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Draw all the lines of symmetry for the following figures.

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Draw all the lines of symmetry for the following figures.

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Draw all the lines of symmetry for the following figures.

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Draw all the lines of symmetry for the following figures.

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Draw all the lines of symmetry for the following figures.

Reflections

Reflections can also be used on the coordinate plane.

A reflection is a figure that has been flipped over a line of reflection.

EXAMPLE

A

B

Suppose that line segment AB is graphed as shown. If it is reflected over the y-axis, it would look like this:

EXAMPLE

A

B

A’

B’

Notice that the image of the linesegment is a mirror image of theoriginal one. It is as if the paperwere folded on the y-axis and it left an identical imprint on the other side of the axis.

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D

E

F

Graph the image of triangle DEFafter a reflection over the x-axis.

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D

E

F

F’

D’

E’

Try This

Now graph the image of parallelogram ABCD after it isreflected over x = 2

A B

C D

Try This

A B

C D

B’ A’

D’ C’

Line of reflection

Notice that the line of reflection is x = 2. It is asif the paper were folded onthe line x = 2.