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Transformation Geometry Dilations. 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. Let’s take a look….

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what is a dilation
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
Proportionally

Let’s take a look…

And, of course, increasing the circle increases the diameter.

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

So, we always have a circle with a certain diameter. We are just changing the size or scale.

Decreasing the size of the circle decreases the diameter.

We have a circle with a certain diameter.

  • Same shape, Different scale.
which of these are dilations

A

HINT: SAME SHAPE, DIFFERENT SIZE

C

D

B

Which of these are dilations??
scale factor and center of dilation
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.

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

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

scale factor
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
Are the following enlarged or reduced??

C

A

Scale factor of 1.5

D

Scale factor of 3

B

Scale factor of 0.75

Scale factor of 1/5

the object and the image

B’

C’

A’

B

A

C

The Object and the Image
  • 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.

Image

Object

remember
Remember
  • Dilations areenlargementsorreductions.
how do we use scale factor
How do we use scale factor?
  • We can multiply the scale factor by each coordinate:

Scale factor = 1/3

A (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)