For the point $P(10,16)$ and $Q(15,21)$, find the distance $d(P, Q)$ and the coordinates of the midpoint $M$ of the segment $P Q$.

Step 1 ：Given points P(10, 16) and Q(15, 21), we will find the distance d(P, Q) and the coordinates of the midpoint M of the segment PQ.

Step 2 ：Use the distance formula: \(d(P, Q) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Step 3 ：Calculate the distance: \(d(P, Q) = \sqrt{(15 - 10)^2 + (21 - 16)^2} = \sqrt{25 + 25} = \sqrt{50}\)

Step 4 ：Use the midpoint formula: \(M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\)

Step 5 ：Calculate the midpoint: \(M = (\frac{10 + 15}{2}, \frac{16 + 21}{2}) = (12.5, 18.5)\)

Step 6 ：Final Answer: The distance \(d(P, Q) = \boxed{\sqrt{50}}\) and the coordinates of the midpoint \(M = \boxed{(12.5, 18.5)}\)