translations lesson 9-8. translations translations are used on the coordinate plane. a translation...

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

Try This

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.

Try This

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.