\begin{tabular}{l} A figure has vertices \( P(0,0), Q(4,5), R^{P}(4,1) \) and \( S(6,3) \). \\ The coordinates of the figure, after a dilation with a scale factor of 0.5 are: \\ \( P^{\prime}(0,0), Q^{\prime}( \) \\ (Put one number in each blank space.) \\ \hline\end{tabular}

To find the new coordinates of the points after dilation with a scale factor of 0.5, we can apply the dilation transformation to each vertex. The formula for dilation is: \[ (x', y') = (kx, ky) \] where \( k \) is the scale factor and \( (x, y) \) are the original coordinates of the vertex. For \( P(0,0) \): \[ P' = (0 \times 0.5, 0 \times 0.5) = (0, 0) \] For \( Q(4,5) \): \[ Q' = (4 \times 0.5, 5 \times 0.5) = (2, 2.5) \] For \( R(4,1) \): \[ R' = (4 \times 0.5, 1 \times 0.5) = (2, 0.5) \] For \( S(6,3) \): \[ S' = (6 \times 0.5, 3 \times 0.5) = (3, 1.5) \] Now we can fill in the blank: The coordinates of the figure after dilation with a scale factor of 0.5 are: \( P^{\prime}(0,0), Q^{\prime}(2,2.5), R^{\prime}(2,0.5), S^{\prime}(3,1.5) \). Thus, for the given problem: The coordinates of \( Q^{\prime} \) are \( (2, 2.5) \).