Triangle \( P Q R \) has coordinates \( P(-1,5), Q(1,2) \), and \( R(-3,-1) \). Determine the coordinates of the vertices of the image after a reflection in the \( x \). axis. \( \begin{array}{l}\text { A) } P^{\prime}(-1,-5)\left(Q^{\prime}(1,-2) \text {, and } R^{\prime}(-3,1)\right. \\ \text { D) } P^{\prime}(5,-1), Q^{\prime}(2,-1) \text {, and } R^{\prime}(1,-3) \\ \text { C) } P^{\prime}(1,5), Q^{\prime}(-1,2) \text {, and } R^{\prime}(3,-1) \\ \text { D) } P^{\prime}(-1,-5), Q^{\prime}(-1,-2) \text {, and } R^{\prime}(-3,-1)\end{array} \)

To find the coordinates of the vertices of triangle \( PQR \) after a reflection in the \( x \)-axis, we need to apply the reflection transformation to each vertex. The reflection of a point \( (x, y) \) in the \( x \)-axis results in the point \( (x, -y) \). Let's apply this transformation to each vertex: 1. For point \( P(-1, 5) \): \[ P' = (-1, -5) \] 2. For point \( Q(1, 2) \): \[ Q' = (1, -2) \] 3. For point \( R(-3, -1) \): \[ R' = (-3, 1) \] Now we have the coordinates of the reflected points: - \( P'(-1, -5) \) - \( Q'(1, -2) \) - \( R'(-3, 1) \) Thus, the coordinates of the vertices of the image after the reflection in the \( x \)-axis are: \[ P'(-1, -5), Q'(1, -2), R'(-3, 1) \] Looking at the options provided, the correct answer is: \[ \text{A) } P'(-1, -5), Q'(1, -2), R'(-3, 1) \]