What is a dilation
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What is a Dilation? PowerPoint PPT Presentation


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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?

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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 GeometryDilations


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


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??

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

  • Use graph paper if applicable.


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


Dilations Used Everyday


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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