First we need a set of coordinate axes as a frame of reference:
Construct AG to make an isosceles right triangle ADG.
The perpendicular bisector of AG will pass through D and create the y-axis while AG is effectively the x-axis. The x-y plane is our frame of reference.
The trapezoids are reflections of each other in the y-axis. This means that the x coordinates of all the vertices are additive inverses of each other (if x is the x coordinate of a vertex in T, then -x is the x coordinate in T'). The y-coordinates of the vertices in T' are the same as in T. The common vertex D has x=0 as the x coordinate so is unaffected by the transformation. So for any vertex X(x,y) we have the corresponding vertex X'(-x,y), that is, (x,y)→(-x,y) is the transformation.