Transformation Geometry Dilations

Dilated PowerPoint Slide What is a Dilation? Dilation is a transformation that produces a figure similar to the original by proportionally shrinking or stretching the figure. You 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. Dilated PowerPoint Slide

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?? HINT: SAME SHAPE, DIFFERENT SIZE Which of these are dilations?? C A B D Discuss 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 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. Scale Factor - change in size of the object. Center of Dilation – the very central point of the object. 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 > 1 0 < Scale Factor < 1 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 The 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. 0 < Scale Factor < 1

Are the following enlarged or reduced?? Scale factor of 1.5 Discuss slides before clicking for the answer. A is enlarged. B is reduced. C is enlarged. D is reduced. D Scale factor of 3 B Scale factor of 0.75 Scale factor of 1/5

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 World’s 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.

Remember Dilations are enlargements or reductions. What are some things that you would not mind dilating to make larger or smaller? Answer: Larger: maybe a house, one’s 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.