Given points A (-4.6, -3), B (7, -3.5), C (-5, -4.0), D (3.0, -5) find the coordinates of the midpoint nates of the midpoint P

Given points A (-4.6, -3), B (7, -3.5), C (-5, -4.0), D (3.0, -5) find the coordinates of the midpoint P of the segment CB, angle between straight lines DC and AB?

1. Given:

A (-4; 6; -3);
B (7; -3; 5);
C (-5; -4; 0);
D (3; 0; -5).
2. Coordinates of the midpoint of the aircraft segment:

B (7; -3; 5);
C (-5; -4; 0);
1/2 * ((7; -3; 5) + (-5; -4; 0)) = (1; -3.5; 2.5);
P (1; -3.5; 2.5).
3. Coordinates of vectors DC and AB and the angle between them:

D (3; 0; -5);
C (-5; -4; 0);
DC = (-5; -4; 0) – (3; 0; -5) = (-8; -4; 5);
| DC | = √ (64 + 16 + 25) = √ (64 + 16 + 25) = √105;
A (-4; 6; -3);
B (7; -3; 5);
AB = (7; -3; 5) – (-4; 6; -3) = (11; -9; 8);
| AB | = √ (121 + 81 + 64) = √ (64 + 16 + 25) = √266;
DC * AB = (-8; -4; 5) * (11; -9; 8) = -88 + 36 + 40 = -12;
cos∠ (DC, AB) = (DC * AB) / (| DC | * | AB |) = -12 / (√105 * √266) = -12 / (7√15 * √38) = -12 / (7√570);
∠ (DC, AB) = arccos (-12 / (7√570)) ≈ 94 °.
Sharp angle: 86 °.