Uestion 8 angle \( P Q R \) 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 \( y \) - As. \( \begin{array}{l}\text { A) } P^{\prime}(-1,-5), Q^{\prime}(1,-2) \text {, and } R^{\prime}(-3,1) \\ \text { B) } P^{\prime}(5,-1), Q^{\prime}(2,-1) \text {, and } R^{\prime}(1,-3) \\ \text { C) } P^{\prime}(1,5), Q^{\prime}(-1,2) \text {, and } R^{\prime}(3,-1) \\ \text { D) } P^{\prime}(1,5), Q^{\prime}(1,2) \text {, and } R^{\prime}(3,1)\end{array} \)

To find the coordinates of the vertices after a reflection in the \( y \)-axis, we need to change the sign of the \( x \)-coordinates of each point while keeping the \( y \)-coordinates the same. Given the points: - \( P(-1, 5) \) - \( Q(1, 2) \) - \( R(-3, -1) \) We will reflect each point across the \( y \)-axis: 1. For point \( P(-1, 5) \): - The reflection is \( P' = (1, 5) \). 2. For point \( Q(1, 2) \): - The reflection is \( Q' = (-1, 2) \). 3. For point \( R(-3, -1) \): - The reflection is \( R' = (3, -1) \). Thus, the coordinates of the reflected points are: - \( P'(1, 5) \) - \( Q'(-1, 2) \) - \( R'(3, -1) \) Now, let's compare these results with the provided options: - A) \( P'(-1, -5), Q'(1, -2), R'(-3, 1) \) - B) \( P'(5, -1), Q'(2, -1), R'(1, -3) \) - C) \( P'(1, 5), Q'(-1, 2), R'(3, -1) \) - D) \( P'(1, 5), Q'(1, 2), R'(3, 1) \) The correct answer is: **C) \( P'(1, 5), Q'(-1, 2), R'(3, -1) \)**.