Detailed description

Cartesian plane. Three rectangles are shown, ABCD, $$A^\prime B^\prime C^\prime D^\prime$$, $$A^{\prime\prime} B^{\prime\prime} C^{\prime\prime} D^{\prime\prime}$$.

Coordinates of ABCD:

A(0, 0), B(0, 4), C(2, 4), D(2, 0).

Rectangle $$A^\prime B^\prime C^\prime D^\prime$$ is the image of ABCD under a rotation of $$30 ^\circ$$ in an anticlockwise direction.
Rectangle $$A^{\prime\prime} B^{\prime\prime} C^{\prime\prime} D^{\prime\prime}$$ is the image of ABCD under a translation of 6 to the right and 1 up.