Transformations: Dilation

Unit 4.04

Vocabulary Dilation: A transformation in which a

figure is made larger or smaller with respect to a point called the center of dilation.

Example: The red polygon has been Dilated (made larger) to form the blue polygon.

Vocabulary Center of Dilation: The point from

which a figure is dilated. When graphed on the Cartesian Plane, the Origin is often the Center of Dilation.

Example: Here, the Origin (0, 0) is the Center of Dilation.

Center of Dilation (0, 0)

Vocabulary Scale Factor: In a dilation, the original

figure and dilated image are similar. The ratio that compares the one with the other is called the Scale Factor and is called k.

Example: The blue square is twice the size of the red square. If red blue, then what is the scale factor?What if blue red?

k = 2k = ½

Vocabulary Dilation on the Cartesian Plane: To

dilate a figure in respect to the origin, multiply the coordinates of each vertex by the scale factor, k.

Vocabulary Dilation on the Cartesian Plane: To

dilate a figure in respect to the origin, multiply the coordinates of each vertex by the scale factor, k.

Transformation Notation of Dilations: (x, y) (kx, ky)

Classifying a Dilation by the Scale Factor: When k > 1, the dilation is an

enlargement When 0 < k < 1, the dilation is a

reduction

Vocabulary Example 1: Dilate ΔABC by the scale

factor, k = 3, then classify it.

Vocabulary Example 2: Dilate Rectangle WXYZ by the

scale factor, k = ½ (or 0.5), then classify it.

You Try It!

1) Dilate ΔABC by a scale factor, k = 2, then classify it.

(1,3)A: _____________

B: _____________

C: ____________

A’: ____________

B’: ____________

C’: ____________

(4,0)(-3,-2)(2,6)(8,0)(-6,-4)

A

B

C

A’

B’

C’

2) Dilate ΔXYZ by a scale factor, k = 1/3, then classify it.

(3,9)X: _____________

Y: _____________

Z: _____________

X’: ____________

Y’: ____________

Z’: ____________

(9,0)(-3,-3)(1,3)(3,0)(-1,-1)

X

Y

Z

X’

Y’

Z’

3) Dilate ΔJKL by a scale factor, k= 2. Then translate it down 5 and to the right 5 units.

KL

J

K’

L’

J’

J’: ____________K’: ____________L’: ____________J’’: ___________K’’: ___________L’’: ____________

(-1,-2) (2,1) (-5,3)(-2,-4)(4,2)

(-10,6)

J: ____________ K: ____________ L: ____________

(3,-9)(9,-3)(-5,1)

K’’

L’’

J’’

Homework Time Scale It! -- Dilations WS