Find the length of the median AM of the triangle ABC given by the coordinates of its vertices A (1,0,2), B (1,0,4) C (-1,0,0)

Decision.
Point M – the middle of the BC side has coordinates:
M ((xB + xC) / 2; (yB + yC) / 2; (zB + zC) / 2);
M ((1 + (-1)) / 2; (0 + 0) / 2; (4 + 0) / 2);
M (0; 0; 2).
To determine the length of the median AM of the triangle ABC, we use the formula to find the distance between two points A1 (x1; y1; z1) and A2 (x2; y2; z2):
A1A2 = √ ((xA2 – xA1) ^ 2 + (yA2 – yA1) ^ 2 + (zA2 – zA1) ^ 2);
AM = √ ((xM – xA) ^ 2 + (yM – yA) ^ 2 + (zM – zA) ^ 2);
AM = √ ((0 – 1) ^ 2 + (0 – 0) ^ 2 + (2 – 2) ^ 2) = 1.
Answer. AM = 1.