For each figure, which placement of the axes shown would be the best to prove properties about the object?

Because the axes are defined by x- and y- coordinates, it is best to place the key dimensions of the figures as either horizontal or vertical lengths.
1. Rectangle - third figure is best, as the length and width are on the axes.
2. Circle - first figure is best, since the center is on the axis and one end of the diameter is at the origin.
3. Equilaterial Triangle - third figure is best, since 1 vertex is at the origin and another is on the x-axis.
4. Isosceles Triangle - first figure is best, since the height is immediately visible as the y-coordinate, and the other vertex is on the x-axis. (Note that unlike #3, there is no choice of the triangle having 1 vertex at the origin.)
5. Trapezoid - second figure is best, since 1 vertex is at the origin and the longest base is along the x-axis, while the other base is also parallel to the x-axis and its length can easily be measured (unlike the third figure, where the base lengths are diagonal and will be so difficult to determine).