(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 that the distance between P and P_2 is the same.
(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.)
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