# Find the length of the segment AB and the coordinates of its midpoint if ta with coordinates

September 30, 2021 | education

| **Find the length of the segment AB and the coordinates of its midpoint if ta with coordinates (1; 3; 4), and тB with coordinates (-1; 4; 2)**

Find the length of the segment AB if the coordinates of the points are known.

T. A (1; 3; 4);

T. B (-1; 4; 2).

| AB | = √ ((x2 – x1) ² + (y2 – y1) ² + (z2 – z1) ²) = √ ((- 1 – 1) ² + (4 – 3) ² + (2 – 4) ²) = √ ((- 2) ² + (1) ² + (-2) ²) = √) 4 + 1 + 4) = √9 = √3² = 3;

Let’s find the coordinates of its midpoint of the segment AB.

С (x; y; z) – coordinates of the midpoint of the segment AB.

x = (1 + (-1)) / 2 = 0/2 = 0;

y = (3 + 4) / 2 = 7/2 = 3.5;

z = (4 + 2) / 2 = 6/2 = 3;

Answer: | AB | = 3.

C (0; 3.5; 3).

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