The coordinates of the vertices of the triangle are known, point A (2; -1; 3), B (-3; 5; 2), C (-2; 3; -5),

The coordinates of the vertices of the triangle are known, point A (2; -1; 3), B (-3; 5; 2), C (-2; 3; -5), BM-median, triangle ABC, find the length of the median BM, calculate the perimeter

Given the coordinates of the vertices of the triangle point A (2; – 1; 3), B (- 3; 5; 2), C (- 2; 3; – 5), BM-median, triangle ABC, we need to find the length of the median BM and calculate the perimeter. Let’s find the median first. We know point M is the middle of the AC. Find the middle of the speaker.

M ((2-2) / 2; (- 1 + 3) / 2; (3 – 5) / 2) = M (0; 1; – 1).

Let’s compose the VM using B (- 3; 5; 2) and M (0; 1; – 1).

VM (0 + 3; 1 – 5; – 1 – 2) = VM (3; – 4; – 3).

Now let’s find the length of the VM:

BM = (9 + 16 + 9) ^ (1/2) = (34) ^ (1/2) ~ 5.8.

In order to find the perimeter of a triangle, we need to compose the sides of the triangle:

AB (- 5; 6; – 1); AC (- 4; 4; – 8) and BC (1; – 2; – 7).

Find the sides of the triangle:

AB = (25 + 36 + 1) ^ (1/2) = (62) ^ (1/2) ~ 7.9;

AC = (16 + 16 + 64) ^ (1/2) = (96) ^ (1/2) ~ 9.8;

BC = (1 + 4 + 49) ^ (1/2) = (54) ^ (1/2) ~ 7.3.

Perimeter of a triangle

P = 7.9 + 9.8 + 7.3 = 25.

Answer: VM ~ 5.8 and P ~ 25.