\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
An affine transformation is defined by \(\mathbf{x}' = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}\mathbf{x} + \begin{pmatrix} 2 \\ 1 \end{pmatrix}\).
  1. Find the image of the origin \(O(0, 0)\).
  2. Find the image of the point \(A(2, 0)\).
  3. Describe the transformation geometrically.

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.