Graph and then rotate rectangle WXYZ with vertices W(-3,-5), X(1,-1),Y(3,-3) and Z(-1,-7) around the origin under the three rotations given below. You must graph the preimage and each image and identify all points from the images. (a) 90^circ counterclockwise (b) 180^circ (c) 270^circ counterclockwise

To rotate a point counterclockwise about the origin, we can use the following rotation matrix: where is the angle of rotation in degrees.(a) counterclockwise rotation: Let's apply this rotation matrix to each vertex of the rectangle WXYZ: So, the vertices of the rotated rectangle W'X'Y'Z' are: (b) rotation: Let's apply this rotation matrix to each vertex of the rectangle WXYZ: So, the vertices of the rotated rectangle W''X''Y''Z'' are: (c) counterclockwise rotation: Let's apply this rotation matrix to each vertex of the rectangle WXYZ:$W''' = R(270^{\circ}) \cdot W = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \cdot \begin{pmatrix} -3 \\ -5 \end{pmatrix} = \