\( \triangle Q R S \) contains the \( -: Q(4,2), R(5,1) \), and \( S(3,7) \). If the \( \Delta \) is reflected across the \( y \)-axis, what will \( S^{\prime} \) be? Select one: a. \( S^{\prime}(3,7) \) b. \( S^{\prime}(3,7) \) c. \( S^{\prime}(-3,7) \) d. \( S^{\prime}(-3,-7) \)

To find the coordinates of point \( S' \) after reflecting point \( S(3,7) \) across the \( y \)-axis, we follow these steps: 1. **Understanding Reflection Across the \( y \)-Axis**: - When a point \( (x, y) \) is reflected across the \( y \)-axis, its \( x \)-coordinate changes sign while the \( y \)-coordinate remains the same. - Therefore, the reflection of point \( S(3, 7) \) will be \( S'(-x, y) \). 2. **Applying the Reflection**: - For point \( S(3, 7) \): - The \( x \)-coordinate is \( 3 \), so after reflection, it becomes \( -3 \). - The \( y \)-coordinate remains \( 7 \). 3. **Resulting Coordinates**: - Thus, the coordinates of \( S' \) after reflection are \( S'(-3, 7) \). Now, let's check the options provided: - a. \( S^{\prime}(3,7) \) - b. \( S^{\prime}(3,7) \) - c. \( S^{\prime}(-3,7) \) - d. \( S^{\prime}(-3,-7) \) The correct answer is: **c. \( S^{\prime}(-3,7) \)**.