Dilations and Similarity

Mr. Saucedo - GEOMETRY - Milby High School

OBJECTIVE:

•To identify and construct dilations.

• A dilation is a transformation that changes the size of a figure but not its shape.

• A scale factor describes how much the figure is enlarged or reduced. For a dilation with scale factor k, you can find the image of a point by multiplying each coordinate by

k: (a, b) → (ka, kb) .

0

A B

CD

A’ B’

C’D’

0

KEY CONCEPT:

• A Dilation stretches or shrinks a figure.

• The Center of Dilation never changes position. It’s a starting point.

• The Scale Factor tells you how much the dilation stretches or shrinks.

• If the scale factor of a dilation is greater than 1 (k > 1) , it is an enlargement. If the scale factor is less than 1 (k < 1) , it is a reduction.

IDENTIFY THE DILATION• Tell whether each transformation is a dilation

A. B.

The transformation is a dilation.

The transformation is not a dilation. The figure is distorted.

DRAWING A DILATION• Draw a dilation

of quadrilateral ABCD, with vertices A(2,1), B(4,1), C(4,-1), and (1,-1). Use a scale factor of k=2.

DRAW A DILATION• A triangle has

the vertices A(4,-4), B(8,2), and C(8,-4). Draw its dilation with a scale of ½.

CAN YOU FIND THE SCALE FACTOR?

FIND THE DILATION FACTOR:From triangle A to B.

Find the scale factor from the Red square to the pink square:

One last thing…

Image Pre-Image

NEW OLD

OR

INDEPENDENT PRACTICE

HOMEWORK

Workbook, Section 6.7. Pages: 121-123Problems: 2, 4, 6, 8, 9, 10, 11, 12, 13Pre AP: Add problem 14.