\( \overline{P Q} \) has a midpoint at \( M(-1,13) \). Point \( P \) is at \( (-14,8) \). Find the coordinates of point \( Q \). Write the coordinates as decimals or integers. \( Q=(\square) \)

To find the coordinates of point \( Q \), we can use the midpoint formula. The midpoint \( M \) of a segment \( \overline{PQ} \) can be calculated as: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Here, \( P = (-14, 8) \) and \( M = (-1, 13) \). Let \( Q \) be \( (x, y) \). Setting up the equations using the midpoint coordinates: For the x-coordinates: \[ -1 = \frac{-14 + x}{2} \] Multiplying both sides by 2 gives: \[ -2 = -14 + x \] Solving for \( x \) results in: \[ x = 12 \] For the y-coordinates: \[ 13 = \frac{8 + y}{2} \] Again, multiplying both sides by 2 results in: \[ 26 = 8 + y \] Solving for \( y \) yields: \[ y = 18 \] Thus, the coordinates of point \( Q \) are: \[ Q = (12, 18) \]