Students examine the effects of dilating figures from two different centers. By experimental verification, they examine the impact on the two dilations of having two different scale factors, the same two scale factors, and scale factors whose product equals . Each of the parameters of these cases provides information on the centers of the dilations, their scale factors, and the relationship between individual dilations versus the relationship between an initial figure and a composition of dilations.
Students must consider how to prove that dilations map segments to segments when the segment is not tied to the coordinate plane. We again call upon our knowledge of the triangle side splitter theorem to show that a dilation maps a segment to a segment. The goal of the lesson is for students to understand the effect that dilation has on segments, specifically that a dilation will map a segment to a segment so that its length is times the original.
Teacher and Student versions of full lesson from engageNY