\( \overline{P Q} \) is reflected across the line \( x=-3 \). The coordinates of the endpoints of the image of \( \overline{P Q} \) are \( P^{\prime}(5,2) \) and \( Q^{\prime}(2,4) \). What are the coordinates of \( Q \) ? \( \begin{array}{l}\text { A }(1,4) \\ \text { B }(-3,4) \\ \text { C }(5,4) \\ \text { D }(-8,4)\end{array} \)

To find the coordinates of point \( Q \) before reflection, we need to determine the coordinates of the original point \( Q \) which, when reflected across the line \( x = -3 \), results in the point \( Q' (2, 4) \). The formula for reflecting a point \( (x, y) \) across the line \( x = c \) is: 1. Calculate the distance from the point to the line, which is \( x - c \). 2. Take double this distance in the opposite direction from the line to get the reflected point. For point \( Q' (2, 4) \) reflecting over the line \( x = -3 \): 1. The line \( x = -3 \) means \( c = -3 \). 2. Distance from \( Q' \) to the line is \( 2 - (-3) = 5 \). 3. Therefore, original point \( Q \) needs to be \( 5 \) units to the left of \( x = -3\): \[ -3 - 5 = -8 \] Thus, the coordinates of point \( Q \) are \( (-8, 4) \). So the answer is: **D** \((-8, 4)\)