[b]Explore dilations on the following graph. Answer the following questions below. [/b][br][br]1. How does the scale factor influence the location of the pre-image and corresponding image points with regards to the center?[br][br]2. How does the scale factor and center influence the length of the pre-image sides and their corresponding image sides.[br][br]3. How does the scale factor and center influence the location of the image with regards to the pre-image.[br][br]4. Other relationships between the pre-image, image, scale factor and center.[br]
[b]Explore dilations on the following graph. Answer the following questions below. [/b][br][br]1. Using the graph below, find the relationship between the scale factor and the ratio of the image's area to the pre-image's area.[br][br]2. Using the graph below, find the relationship between the scale factor and the ratio of the perimeter of the image to the perimeter of the pre-image.[br]
In the graph below, measure the distances of segments A' B' and AB. What is the relationship between these two distances, and how does it relate to the scale factor? [br][br]Does this relationship exist between all the sides of the triangles? How do you know?
1. In the graph above, find the slope of each side of triangle â–²ABC and triangle â–²A'B'C', what do you notice? [br][br]2. Move the pre-image and center of dilation around, does this change the relationship between the slopes? [br][br]3. Move point C on top of the center of dilation; how does this change the relationship between the sides of the triangles?
In the graph below, measure the angles of â–² ABC and â–²A'B'C. What do you notice? [br][br]Move the center of dilation around and tell me if the relationship between the image and pre-image angles changes.
In the graph below, what is the domain and range of the dilation function?
Using the graph below, write a two-variable function to describe the dilation f(x,y)-->( , ). Justify your response.
In the graph below, move the center of dilation away from the origin (away from point 0,0). Write a two-variable function to describe the dilation when the center is not at the origin f(x,y)-->( , ). Justify your response.