Exploring Dilation in the Coordinate Plane

Explore dilations on the following graph. Answer the following questions below. 1. How does the scale factor influence the location of the pre-image and corresponding image points with regards to the center? 2. How does the scale factor and center influence the length of the pre-image sides and their corresponding image sides. 3. How does the scale factor and center influence the location of the image with regards to the pre-image. 4. Other relationships between the pre-image, image, scale factor and center.

Explore dilations on the following graph. Answer the following questions below. 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. 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.

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? 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 ▲ABC and triangle ▲A'B'C', what do you notice? 2. Move the pre-image and center of dilation around, does this change the relationship between the slopes? 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 ▲ ABC and ▲A'B'C. What do you notice? 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.