int \( Q \) is on line segment \( \overline{P R} \). Given \( P R=16 \) and \( P Q=4 \), determine the length \( \overline{Q R} \).

To find the length of \( \overline{Q R} \), we start with the information given: - The total length of segment \( \overline{P R} \) is \( PR = 16 \). - The length of segment \( \overline{P Q} \) is \( PQ = 4 \). Since point \( Q \) is on the line segment \( \overline{P R} \), we can express the length of segment \( \overline{Q R} \) in terms of the lengths of \( \overline{P R} \) and \( \overline{P Q} \). Using the relationship between the segments, we have: \[ PR = PQ + QR \] Substituting the known values into the equation: \[ 16 = 4 + QR \] To isolate \( QR \), we subtract \( 4 \) from both sides: \[ QR = 16 - 4 \] Calculating the right side gives: \[ QR = 12 \] Thus, the length of \( \overline{Q R} \) is \[ \boxed{12} \]