(688,#23) Find the lengths of the medians of the triangle with vertices A(1,2,3), B(-2,0,5) and C(4,1,5).

Solution:

Determine the midpoint of each line segment:

Midpoint of AB:

Midpoint of AC:

Midpoint of BC:

2) Determine length of each median:

Distance formula in three dimensions for the distance between the points
is:

Length of median #1 (blue) is distance between the point B (-2,0,5) and the midpoint(5/2,3/2,4) of the line segment AC:

Length of median #2 (green) is the distance between the point A(1,2,3) and the midpoint(1,1/2,5) of the line segment BC:

Length of the median#3 (magenta) is the distance between the point C(4,1,5) and the midpoint (-1/2,1,4) of the line segment AB:

by:sh