Triangle \( J K L \) has coordinates \( J(2,-5), K(-1,-3) \), and \( L(-4,5) \), Determine the coordinates of the vertices of the image after a rotation \( 270^{\prime} \) counterclockwise about the origin. \( \begin{array}{l}\text { A) } J^{\prime}(2,5), K^{\prime}(-1,3) \text {, and } L^{\prime}(-4,-5) \\ \text { B) } J^{\prime}(5,2), K^{\prime}(3,-1) \text {, and } L^{\prime}(-5,-4) \\ \text { C) } J^{\prime}(-5,-2), K^{\prime}(-3,1) \text {, and } L^{\prime}(5,4) \\ \text { D) } J^{\prime}(-2,5), K^{\prime}(1,3) \text {, and } L^{\prime}(4,-5)\end{array} \)

To find the coordinates of the vertices of triangle \( J K L \) after a \( 270^\circ \) counterclockwise rotation about the origin, we can use the rotation transformation formula. The transformation for a \( 270^\circ \) counterclockwise rotation is given by: \[ (x, y) \rightarrow (y, -x) \] We will apply this transformation to each vertex of the triangle. 1. For point \( J(2, -5) \): \[ J' = (-5, -2) \] 2. For point \( K(-1, -3) \): \[ K' = (-3, 1) \] 3. For point \( L(-4, 5) \): \[ L' = (5, 4) \] Now we have the new coordinates after the rotation: - \( J'(-5, -2) \) - \( K'(-3, 1) \) - \( L'(5, 4) \) Thus, the coordinates of the vertices of the image after the rotation are: \[ J'(-5, -2), K'(-3, 1), L'(5, 4) \] Looking at the options provided, the correct answer is: **C) \( J'(-5, -2), K'(-3, 1), L'(5, 4) \)**.