Getting Started… 9.6 - Translations Find y (figure not drawn to scale!): 5yº 9yº92º 139º 71º Y = 17.

Getting Started…9.6 - Translations

• Find y (figure not drawn to scale!):

5yº

9yº 92º

139º71º

Y = 17

Translation (Slide)

The action of sliding a figure in any direction.

The act of sliding a figure in any direction.

Reflection (flip - mirror)

The result of a figure flipped over a line.

The result of a figure flipped over a line.

Rotation(Turn)

The action of turning a figure around a point or a

vertex.

Turning a figure around a point or a vertex

Terminology

• Image – final image after transformation

Labeled with “Prime”

• Pre-image – image before transformation

Labeled with Capital Letters

A A’

B B’

Pre-Image Image

Horizontal Translation

Translation

Pre-ImageImage Slide Arrow

A

BC

A’

B’ C’

Algebraic Translations

• Let B have coordinates (2,5). Find the image of B after the following translation:

– Left 4 units , up 2 units:

– Right 5 units, down 9 units:

(-2, 7)

(7, -4)

Try some more!

• Let point C have the coordinates (-4,1). Find the image coordinates C for each translation.

• - (x,y) (x + 3, y – 1)

• -(x,y) (x – 2, y + 5)

(-1, 0)

(-6, 6)

5

4

3

2

1 -5 -4 -3 -2 -1

-11 2 3 4 5

-2

-3

-4

-5

Find the image coordinates for each translation(x, y) → (x-5, y)

A

B

C

B

AC

5

4

3 2

1

-5 -4 -3 -2 -1 -1

1 2 3 4 5

-2

-3

-4

-5

Find the image coordinates for each translation(x, y) → (x-1, y + 3)

AB

C D

B A

CD

Triangle ABC has vertices A(–2, 1), B(2, 4), and C(1, 1).

Find the coordinates of the vertices of the image if it is translated 3 units to the right and 5 units down.

Answer: The coordinates of the vertices of the image are A(1, –4), B(5, –1), and C(4, –4).

Graph triangle ABC and its image.

Answer:

The preimage is .

A(–2, 1), B(2, 4), and C(1, 1).

The translated image

is A(1, -4), B(5, -1), and C(-4, -4).

A

B

C

A

B

C

Triangle JKL has vertices J(2, –3), K(4, 0), and L(6, –3).a. Find the coordinates of the vertices of the image if it is

translated 5 units to the left and 2 units up.

b. Graph triangle JKL

and its image.

Answer: J(–3, –1), K(–1, 2), L(1, –1)

Answer:

Last One

What is the equation of this line?

Name an equation of a line that is translated vertically 3 units up?

http://www.shodor.org/interactivate/activities/Transmographer/

HomeworkExtra Practice 9.6