Transformation GeometryDilations

What is a Dilation?

Dilation is a transformation that produces a figure similar to the original by proportionally shrinking or stretching the figure.

Dilated PowerPoint Slide

Proportionally

When a figure is dilated, it must be proportionally larger or smaller than the original.

Same shape, Different scale.

Let’s take a look…

We have a circle with a certain diameter.

Decreasing the size of the circle decreases the diameter.

And, of course, increasing the circle increases the diameter.So, we always have a circle with a certain diameter. We are just changing the size or scale.

Which of these are dilations??

AC

D

B

HINT: SAME SHAPE, DIFFERENT SIZE

Scale Factor and Center of Dilation

When we describe dilations we use the terms scale factor and center of dilation.

Scale factor Center of Dilation

Here we have Igor. He is 3 feet tall and the greatest width across his body is 2 feet.

He wishes he were 6 feet tall with a width of 4 feet.

He wishes he were larger by a scale factor of 2.

His center of dilation would be where the length and greatest width of his body intersect.

Scale Factor If the scale factor is larger than 1, the

figure is enlarged. If the scale factor is between 1 and 0, the

figure is reduced in size.

Scale factor > 1

0 < Scale Factor < 1

Are the following enlarged or reduced??

AC

DB

Scale factor of 0.75

Scale factor of 3

Scale factor of 1/5

Scale factor of 1.5

The Object and the Image

A’

A

B

B’

C’

C

The original figure is called the object and the new figure is called the image.

The object is labeled with letters.

The image may be labeled with the same letters followed by the prime symbol.

Object

Image

Dilations Used Everyday

Remember

Dilations are enlargements or reductions.

How do we use scale factor?

We can multiply the scale factor by each coordinate:

Scale factor = 1/3A (3, 9) , B (15, -6), C (6, 0)

1/3 * A(3, 9) A’ (1, 3) 1/3 * B(15, -6) B’ (5, -2) 1/3 * C(6, 0) C’ (2, 0)