(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 ( x 1 + x 2 2 , y 1 + y 2 2 , z 1 + z 2 2 ) (b) 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.)
(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 ( x 1 + x 2 2 , y 1 + y 2 2 , z 1 + z 2 2 ) (b) 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.)
(a) Prove that the midpoint of the line segment from P1(x1, y1, z1) to P2(x2, y2, z2) is
(
x
1
+
x
2
2
,
y
1
+
y
2
2
,
z
1
+
z
2
2
)
(b) 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.)
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