The vertices of the triangle ABC have coordinates: A (-1; 2; 3) B (1; 0; 4) C (3; -2; 1).

| April 9, 2021 | education

The vertices of the triangle ABC have coordinates: A (-1; 2; 3) B (1; 0; 4) C (3; -2; 1). find the length of the middle triangle parallel to side AB

Let MN be the middle line (M belongs to BC, and N belongs to AC).

By the property of the middle line, M is the middle of BC and N is the middle of AC.

Find the coordinates of the midpoint of the segments by the formula ((x1 + x2) / 2; (y1 + y2) / 2; (z1 + z2) / 2).

Find the coordinates of point M, midpoint BC: B (1; 0; 4), C (3; -2; 1).

M = ((1 + 3) / 2; (0 – 2) / 2; (4 + 1) / 2) = (2; -1; 2.5).

Let’s find the coordinates of the point N, the middle of the AC: A (-1; 2; 3), C (3; -2; 1).

N = ((-1 + 3) / 2; (2 – 2) / 2; (3 + 1) / 2) = (1; 0; 2).

The length of the segment is calculated by the formula d² = (x2 – x1) ² + (y2 – y1) ² + (z2 – z1) ².

Find the length of MN: M (2; -1; 2.5), N (1; 0; 2).

| MN | = √ ((1 – 2) ² + (0 – (-1)) ² + (2 – 2.5) ²) = √ (1 + 1 + 0.25) = √2.25 = 1.5.

Answer: the length of the middle line is 1.5 units. segment.



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