Complex Numbers and Transformations

In the figure below, point A and the vertices of the triangle are complex numbers. Every point on the triangle is being added with point A. This induces a Transformation. Drag Point A around. Under what conditions is the transformation a dilation? Under what conditions is the transformation a translation? Under what conditions is the transformation a rotation? Under what conditions is the transformation a reflection? Under what conditions is the transformation a composition of a rotation and a dilation?