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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…. - PowerPoint PPT Presentation

Slide 1

Transformation GeometryDilations

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 Slide2You are probably familiar with the term dilate in reference to the eye doctor.When doctors dilate your eyes, they are making the pupils larger for a better view of the back if the eye.

ProportionallyWhen a figure is dilated, it must be proportionally larger or smaller than the original.Same shape, Different scale.Lets take a lookWe have a circle with a certain diameter.Decreasing the size of the circle decreases the diameter.And, of course, increasing the circle increases the diameter.So, we always have a circle with a certain diameter. We are just changing the size or scale.Which of these are dilations??

A

C

D

BHINT: SAME SHAPE, DIFFERENT SIZE4Discuss slides before clicking for the answer.A is not a dilation because the milk containers are not the same shape.B is a dilation because it is the same image, same size just a different scale or size.C is a dilation because it is the same image, same size just a different scale or size.D is not a dilation because the baby duck is not just a smaller replication as the mother duck since it is not the same size.Scale Factor and Center of DilationWhen 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.He wishes he were larger by a scale factor of 2.

His center of dilation would be where the length and greatest width of his body intersect.5Scale Factor - change in size of the object.Center of Dilation the very central point of the object.Scale FactorIf 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 > 10 < Scale Factor < 16The length of each side of the new image is equivalent to the length of the corresponding side of the original figure multiplied by the scale factor.

Are the following enlarged or reduced??

A

C

D

BScale factor of 0.75Scale factor of 3Scale factor of 1/5Scale factor of 1.57Discuss slides before clicking for the answer.A is enlarged.B is reduced.C is enlarged.D is reduced.The Object and the ImageAABBCCThe 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.ObjectImageDilations Used Everyday

9Worlds Largest Arcade Game enlarged in size for fun.Toy cars - reduced in size for play.Large Chair enlarged to capture attention as a furniture store sign. Maps reduced in sized for practicality or use.Models reduced in size for the sight of the overview of the building for modeling.Large Burger enlarged in size for fun.RememberDilations are enlargements or reductions.

10Answer: Larger: maybe a house, ones favorite food, a bed, a television. Smaller: maybe favorite animal like an elephant, a car to fit into pocket, items needed to be put in storage.How do we use scale factor?We can multiply the scale factor by each coordinate:

Scale factor = 1/3A (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)

11Answer: Larger: maybe a house, ones favorite food, a bed, a television. Smaller: maybe favorite animal like an elephant, a car to fit into pocket, items needed to be put in storage.