This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and drawing. The researcher identified different purposes for which students used dragging and different purposes for which students used measures. These purposes appeared to be influenced by students' mathematical understandings that were reflected in how they reasoned about the physical representations, the types of abstractions they made, and the reactive or proactive strategies employed.