Transformation Geometry Dilations

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# Transformation Geometry Dilations - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Transformation Geometry Dilations' - hanzila

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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…

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.

A

HINT: SAME SHAPE, DIFFERENT SIZE

C

D

B

Which of these are dilations??
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
• 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??

C

A

Scale factor of 1.5

D

Scale factor of 3

B

Scale factor of 0.75

Scale factor of 1/5

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
• Dilations areenlargementsorreductions.
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)