Translations 3-1D

What is the definition of a translation?

What are some uses of translations?

Is there a connection between translations and vectors?

Definition

A translation is a transformation that moves all the points in a plane a fixed distance in a given direction (slide).

Translations

The arrow shows the direction of the translation.

Translation vectorSince vectors have a distance and a direction,

they are often used to describe translations.

The vector shows the direction of the translation and its length gives the distance each point travels.

To measure direction, add a horizontal dotted line and measure counterclockwise

Find the translation image of each of the following using vector PQ

1. Point L

2. Segment AB

3. Segment MN

4. Triangle LMN

5. Point B

1.Point Y

2.Segment CD

3.Segment XZ

4.Triangle YXZ

5.Point D

M

NL

X

Y Z

P

QA

B

C

D

Translate It page 172

P

Q

M

N

6

3Vector

<3,6>

(2,4)

(−1,−2)

x’s 2−(−1) = 3

y’s 4−(−2) = 6

Try It

The translation image of A (4, −2) is B (5,2). Give the translation vector and the coordinates of the image of C (−1,4).

Translation vector is <1,4>

5 − 4 = 1 2 −(−2) = 4

C’ = (0,8)

−1 + 1 = 0 4 + 4 = 8

Translations change only the location of a figure.

Translations preserve any property that has to do with the size of a figure including:

• The lengths of its sides• The measure of its

angles• The area and perimeter

of the figure

Translations also preserve the orientation of the figure.

• What is the definition of a translation?

A translation is a transformation that moves all the points in a plane a fixed distance in a given direction.

• What are some uses of translations?

Patterns are created by translations.

• Is there a connection between translations and vectors?

Since vectors have a distance and a direction, they are often used to describe translations.

Assignment 3-1D

Page 173, 1-15

What is the translation vector for problems12-15?