What is a dilation
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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. Transformation Geometry Dilations. 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


Using the scale factor to dilate
Using the scale factor to dilate

  • A triangle has vertices A(4, -4), B(8,2) and C(8, -4). The image of triangle ABC after a dilation with a scale factor of ½ is triangle DEF. Find the coordinates and sketch the graph.


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


Book practice pg 412 5 10 12
Book Practice pg 412 #5, 10, 12

  • Use graph paper if applicable.


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.

  • What are some things that you would not

    mind dilating to make larger or smaller?

    Practice Dilation Quiz


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