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What is a Dilation?

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

Dilated PowerPoint Slide

Transformation GeometryDilations

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

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.

- 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

- 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.

C

A

Scale factor of 1.5

D

Scale factor of 3

B

Scale factor of 0.75

Scale factor of 1/5

- Use graph paper if applicable.

B’

C’

A’

B

A

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.

Image

Object

- Dilations areenlargementsorreductions.
- What are some things that you would not
mind dilating to make larger or smaller?

Practice Dilation Quiz