1. The problem states that point \mathbf{R} was translated by the vector \begin{pmatrix} 4 \\ -3 \end{pmatrix} to get point \mathbf{R}'. 2. Translation means adding the vector to the original point coordinates: $$\mathbf{R}' = \mathbf{R} + \begin{pmatrix} 4 \\ -3 \end{pmatrix}$$ 3. We know \mathbf{R}' = (-1, 1), so: $$\begin{pmatrix} -1 \\ 1 \end{pmatrix} = \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} 4 \\ -3 \end{pmatrix}$$ 4. To find \mathbf{R} = (x, y), subtract the translation vector from \mathbf{R}': $$\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -1 \\ 1 \end{pmatrix} - \begin{pmatrix} 4 \\ -3 \end{pmatrix} = \begin{pmatrix} -1 - 4 \\ 1 - (-3) \end{pmatrix} = \begin{pmatrix} -5 \\ 4 \end{pmatrix}$$ 5. Therefore, the coordinates of point \mathbf{R} are $(-5, 4)$.