1. Choose a number between 2 and 10. This is the length of a line segment. If you dilate the line segment by a factor of 3, what is the relationship between the lengths of the line segment and its dilation? How would you describe the relationship of dilation to the original?
2. Choose another number between 2 and 10. This is the length of one side of a cube. If you dilate the cube by a factor of 2, what is the relationship between the volume of the cube and its dilation? What if the cube is a sphere or a pyramiddoes the relationship of the volumes change?
3. Television sets used to come with an aspect ratio of 4:3 (width is 4 units and height is 3 units). Since broadcast channels in the United States are now broadcasting in 16:9, most newer sets come with a 16:9 aspect ratio. Your brother believes that since you can rewrite the ratio 16:9 as 4²:3², that means a 4:3 television set is similar to a 4²:3²television set. Is this true? What argument would you use to clarify your or your brother's thinking? What are the dimensions of a television set that would be similar to the 4:3 set?