Find the length of the median AM of the triangle ABC, specified by the coordinates of its vertex

Find the length of the median AM of the triangle ABC, specified by the coordinates of its vertex: A (0; -1; 1), B (0; -1; 3), C (-2; -1; -1).

Point M will be in the middle of the BC segment. Find the coordinates of point M:

xm = (xb + xc) / 2 = (0 – 2) / 2 = -1;

ym = (yb + yc) / 2 = (-1 -1) / 2 = -1;

zm = (zb + zc) / 2 = (3 – 1) / 2 = 1;

M (-1; -1; 1).

Distance from point A to point M:

d = √ ((xm – xa) ^ 2 + (ym – ya) ^ 2 + (zm – za) ^ 2) =

= √ ((- 1 – 0) ^ 2 + (-1 – (-1)) ^ 2 + (1 – 1) ^ 2) =

= √ (1 + 0 + 0) = 1.

Answer: 1.