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# (a) Prove that the midpoint of the line segment from $P_1 (x_1, y_1, z_1)$ to $P_2 (x_2, y_2, z_2)$ 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 $A (1, 2, 3)$, $B (-2, 0, 5)$, $C (4, 1, 5)$. (A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.)

## (b) $\frac{5}{2}, \frac{1}{2} \sqrt{94}, \frac{1}{2} \sqrt{85}$

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