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Section 12.1: Three dimenstional Coordinate Geometry

Exercise 21

  1. 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 \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \]
  2. Find the lengths of the medians of the triangle with vertices A(1, 2, 3), B(-2, 0, 5), and C(4, 1, 5). (A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.)