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  When a figure is dilated, it must be proportionally larger or smaller than the original.  Same shape, Different scale. Let’s take a look… We 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 B HINT: SAME SHAPE, DIFFERENT SIZE

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. 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.

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?? A C D B Scale factor of 0.75 Scale factor of 3 Scale factor of 1/5 Scale factor of 1.5

The Object and the Image A’ A B B’ C’ 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. Object Image

Dilations Used Everyday

Remember  Dilations are enlargements or reductions.  What are some things that you would not mind dilating to make larger or smaller? Practice Dilation Quiz