Transformations: Translation

Unit 4.03

Vocabulary Translation: A transformation that

moves every point in a figure the same distance in the same direction.

Example: The blue polygon has been Translated to the right 5 units and up 4 units (landing on the red polygon).

Vocabulary Translation Notation: You can identify

the direction and distance of a translation (aka the translation rule) without seeing a picture of it, simply by writing it in translation notation!

Example:

Blue Red

(x, y) (x+5, y+4)

You Try It!

The translation rule of the BLUE triangle, ΔABC, to the RED triangle, ΔA’B’C’ in Transformation Notation is given.

Write what is happening in

words.

1)

(x, y) (x–4, y+5)

ΔABC was moved left 4 units and up 5 units.

The translation rule of the BLUE square, SERQ, to the RED square, S’E’R’Q’ in Transformation Notation is given.

Write what is happening in

words.(x, y) (x–2, y+3)

2)

Square SERQ was moved 2 units to the left and 3 units up.

The translation rule of the BLUE triangle, ΔTRI, to the RED triangle, ΔT’R’I’ in Transformation Notation is given.

Write what is happening in

words.

(x, y) (x+6, y–4)

3)

ΔTRI was moved to the right 6 units and down 4 units.

Graph the Image of ΔABC according to the given information below:

A(5,5), B(-1,4), C(3,0) and

4)

(x,y) (x–2,y–3) A

C

B

A’B’

C’

Without graphing ΔABC, find the coordinates of ΔA’B’C’ according to the information given below:

A(-3,5), B(1,2), & C(5,4) and

5)

(x,y) (x+4,y–5)

A’(1,0), B’(5,-3), & C’(9,-1)

Vocabulary Transformation (Prime) Notation

cont.: In transformation notation, the use of (‘) designates the translated (moved) Image. Repeated transformations result in (“) and even (“’) being used! (prime, double prime, triple prime) Example: Let’s See how much you know!

1) If A(2, 4) and (x,y)(x+2,y-2), what is A’?

2) * What would A” be?

(4,2)(6,0)

Put It All

Together!

6) Move ΔABC 5 units to the left and 3 units up. List the coordinates below.

(6, 5)A: _____________

B: _____________

C: ____________

A’: ____________

B’: ____________

C’: ____________

(5, -5)

(-2, 1)

(1, 8)

(0, -2)

(-7, 4)

A

B

C

A’

B’

C’

7) Move ΔPQR 6 units down and 4 units to the right. List the coordinates below.

(-5, 7)P: _____________

Q: ____________

R: ____________

P’: ____________

Q’: ____________

R’: ____________

(-2, 4)

(-9, 2)

(-1, 1)

(2, -2)

(-5, -4)

P

Q

RP’

Q’

R’

8) Move ΔXYZ 10 units down and 3 units to the right. Draw both images and list the missing coordinates below.

(1, 9)X: _____________

Y: _____________

Z: ____________

X’: ____________

Y’: ____________

Z’: ____________

(1, 5)

(-9, 2)

(4, -1)

(4, -5)

(-6, -8)

X

Y

Z

X’

Y’

Z’

9) Describe the translation shown below in words. ΔJKL ΔJ’K’L’

K

L

J

K’

L’

J’

ΔJKL was moved 4 units to the left and

7 units up!

Homework Time Slide It! -- Translations WS