Chapter 12.1, Problem 21E

(a) Prove that the midpoint of the line segment from $P_1\left(x_1,y_1,z_1\right)$ to $P_2\left(x_2,y_2,z_2\right)$ is

$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)$

(b) Find the lengths of the medians of the triangle with vertices $A\left(1,2,3\right),B\left(-2,0,5\right),$ and $C\left(4,1,5\right).$ (A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.)