(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.)
Solution Summary: The author explains the formula used to find the distance between two points.
(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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