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.