TRANSLATIONS

THE BASICSVocabulary and concepts

WHAT IS A TRANSLATION?

A transformation that “slides” an object a fixed distance.

Examples:

WHAT IS THE DIFFERENCE BETWEEN A FIGURE AND AN

IMAGE?Figure: The Original Image: The shape after the

transformation takes place

Figure ImageFigure Image

CHARACTERISTICS OF A TRANSLATION

STOP! Answer the true/false questions on your notes while examining the examples of translations below:

Move on to the next slide only AFTER you answer the questions

T F A figure that is translated produces a congruent image.

T F A figure that is translated produces a similar image.

T F A figure that is translated produces an image with the same side lengths.

T F A figure that is translated maintains the same orientation (position).

T F A figure that is translated can only move side to side.

Check Your AnswersThe correct answers are in yellow

HOW DO YOU KNOW WHICH IS WHICH?

The “prime” symbol indicates that is the image, or the shape after

the transformation.

Figure Image

This is the “prime” symbol (it looks like an apostrophe)

LET’S LOOK A LITTLE CLOSER.

Directions: Write the coordinates of the figure. Then, write the coordinates of the image.

A (-4,6)

B (-4,1)

C (-1,1)

Figure Image

A’ (2,8)

B’ (2,3)

C’ (5,3)

Figure: Image:

LET’S DO TRANSLATIONS!What are they again?

WHEN AN IMAGE “SLIDES” IN A GIVEN DIRECTION

HOW DO I KNOW THE DIRECTION IT NEEDS TO GO IN?

Three Ways:

•Words Example:

•Arrow Notation Example:

•Displacement Example:

ALL THREE OF THESE RULES SAY THE SAME THING

Each point moved to the right 4 units, and down 2 units.

• LOOK!

LET’S LOOK AT THE COORDINATES OF THE VERTICES…

Figure: Image:A (-3,4) A’

(1,2)B (0,3) B’

(3,1)

D’ (-3,-1) D’ (1,-3)

C (-1,-1) C’ (3,-

3)

LOOK A LITTLE CLOSER:

The move was:

or

or

Figure:

So…

… 4 was added to the x coordinate

+ (Addition)

- (subtraction)

Add 4 to the x

1 2A’( , )

A (-3,4)

Image:

… 2 was subtracted from the y coordinate

Subtract 2 from the y

LET’S PRACTICEWrite the coordinates of the vertices of the given figure. Then, perform the translation given and find the coordinates of the vertices of the image.

Click me for the answer!

Figure:

B (-3,3)

A (0,4)

T (0,-1)

J (-4,0)

Image:

B’ (-4,1)

A’ (-1,2)

T’ (-1,-3)

J’ (-5,-2)

Write the coordinates of the vertices of the given figure. Then, perform the translation given and find the coordinates of the vertices of the image.

Click me for the answer!

Figure:

W (-1,4)

V (3,0)

T (-1,-1)

Image:

W’ (-1,3)

V’ (3,-1)

T’ (-1,-2)

There is no movement on the x, it doesn’t tell us to do anything, so the x-coordinate stays the same!

Write the coordinates of the vertices of the given figure. Then, perform the translation given and find the coordinates of the vertices of the image.

Click me for the answer!

Figure:

K (-5,-3)

W (-1,0)

F (-3,-4)

Image:

K’ (-2,2)

W’ (2,5)

F’ (0,1)

Below you are given the coordinates of the vertices of a figure and a rule for a translation. What would the coordinates of the image be if the given translation is performed on each figure?

Click me for the answer!

Image:

C’ (-2, -4) J’ (-4, 1) G’ (0,1) P’ (-1,-

3)

Below you are given the coordinates of the vertices of a figure and a rule for a translation. What would the coordinates of the image be if the given translation is performed on each figure?

Click me for the answer!

Image:

Q’ (-2, 1) M’ (-2, 2) G’ (0,2) P’ (-

1,1)

Below you are given the coordinates of the vertices of a figure and a rule for a translation. What would the coordinates of the image be if the given translation is performed on each figure?

Click me for the answer!

Image:

E’ (-2, -4) H’ (-1, 1) G’ (0,0)

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