BUBBLE MAP Thinking Skill Describing word or phrase

BUBBLE MAP Thinking Skill: Describing word or phrase (adjective) Main Idea or Concept Describing word or phrase (adjective)

Math 8 Day 10 Learning Target: Students can define what a dilation is and the process. 1. Dilations 2. Scale Factor

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 Power. Point Slide

Proportionally Let’s take a look… And, of course, increasing When the circle a figure is dilated, it must be proportionally larger or smaller increases the So, we always have a circle with diameter. the original. athan certain diameter. We are just changing Decreasing the size of the circle decreases the diameter. ¡ Same the size or scale. We have a circle with a certain diameter. shape, Different size.

Which of these are dilations? ? A HINT: SAME SHAPE, DIFFERENT SIZE C D B

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 He wishes he were larger by a length and greatest width of his body scale factor of 2. intersect.

Determining Scale Factor:

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

Scale Factor Facts: 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

Ratio Fraction Decimal Percentage Reduction or Enlargement 1: 2 1/2 3/4 . 5 50% Reduction 0. 9 400% 2: 5 1/8

Are the following enlarged or reduced? ? C A Scale factor of 1. 5 D B Scale factor of 0. 75 Scale factor of 1/5 Scale factor of 3

Dilations Used Everyday

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

Dilation A transformation that changes the size of an object, but not the shape. A Dilation will be a similar figure, but not a congruent figure. Example:

Dilate the object by a scale factor of ½ (-2, 2) (2, -2) (-2, -2)

Dilate the object by a scale factor of 3 (-6, 6) (-2, 2) (2, -2) (-2, -2) (6, -6) (-6, -6)