Students should be grouped strategically into groups of 2-4 people with each group or person having a laptop or computer.
Let the students experiment with moving the center of dilation and the pre-image, and how these effect the image resulted in the dilation.
Have them not move their shape for a second and ask them what they think their scale factor is, and ask them to prove it to you with the distance formula or Pythagorean Theorem.
Have them discuss in their group what the relationship between the corresponding sides is. You are hoping for them to determine that one is half the length of the other, but you also want them to discover that they are parallel to each other.
Have them find the slope of corresponding sides and determine if they are the same.
Give them the coordinates of their own shape like A(2,3) B(5,8) C(4,0) and D(2,-2) and have them find the slope of each side. Have them draw a guide line from the center of dilation through one of the points out at least twice the length from the center to the point to find the image point of A which would be A'(4,6) if the scale factor is 2.
Have them use the slopes of the corresponding sides of the pre-image to draw parallel lines from the point A' to extend 2 times as long as AB and AD to find B' and D'.
Continue this process until the entire image is found.
Have students verify that the pre-image is in fact a similar figure using the distance formula.
I recommend that each group be given a different set of points to promote individuality and fidelity of assessment.
Students can also present their graph to the whole class by the use of a document camera.