Quadrilateral \( J K L M \) has vertices at \( J(0,0), K(0,6) \), \( L(9,12) \), and \( M(12,0) \). Find the vertices of the quadrilateral after a dilation with scale factor \( \frac{2}{3} \). \( \begin{array}{l}J^{\prime}(0,0), K^{\prime}(0,9), L^{\prime}(27 / 2,18) \text {, and } M^{\prime}(18,0) \\ J^{\prime}(0,0), K^{\prime}(0,4), L^{\prime}(6,8) \text {, and } M^{\prime}(8,0) \\ J^{\prime}(0,0), K^{\prime}(0,-4), L^{\prime}(-6,-4) \text {, and } M^{\prime}(-8,0) \\ J^{\prime}(2 / 3,2 / 3), K^{\prime}(2 / 3,20 / 3), L^{\prime}(9 / 3,38 / 3) \text {, and } \\ M^{\prime}(38 / 3,2 / 3)\end{array} \)

To find the vertices of quadrilateral \( J K L M \) after a dilation with a scale factor of \( \frac{2}{3} \) centered at the origin, we need to multiply each coordinate of the vertices by \( \frac{2}{3} \). 1. For vertex \( J(0,0) \): \[ J' = \left( \frac{2}{3} \cdot 0, \frac{2}{3} \cdot 0 \right) = (0, 0) \] 2. For vertex \( K(0,6) \): \[ K' = \left( \frac{2}{3} \cdot 0, \frac{2}{3} \cdot 6 \right) = (0, 4) \] 3. For vertex \( L(9,12) \): \[ L' = \left( \frac{2}{3} \cdot 9, \frac{2}{3} \cdot 12 \right) = \left( 6, 8 \right) \] 4. For vertex \( M(12,0) \): \[ M' = \left( \frac{2}{3} \cdot 12, \frac{2}{3} \cdot 0 \right) = (8, 0) \] So the new vertices after dilation are: \[ J^{\prime}(0,0), K^{\prime}(0,4), L^{\prime}(6,8), M^{\prime}(8,0) \] Thus, the correct choice is: \( J^{\prime}(0,0), K^{\prime}(0,4), L^{\prime}(6,8) \text {, and } M^{\prime}(8,0) \).