# Midpoint of a Line Segment

### Midpoint in 3D

If A = (x_{1}, y_{1}, z_{1}) and B = (x_{2}, y_{2}, z_{2}) are the endpoints of a line segment, the midpoint of the line segment is given by:

#### Examples

Calculate the coordinates of the midpoint from the line segment AB.

Calculate the coordinates of Point C in the line segment AC, knowing that the midpoint is B = (2, −2) and an endpoint is A = (−3, 1).

If M_{1} = (2, 1), M_{2 } = (3, 3) and M_{3} = (6, 2) are the midpoints of the sides that make up a triangle, what are the coordinates of the vertices?

x_{1} = 7 x_{5} = 7 x_{3} = −1

y_{1} = 4 y_{5} = 0 y_{3} = 3

A(7, 4)B(5, 0) C(−1, 2)

If the line segment AB with endpoints A = (1,3) and B = (7, 5) is divided into four equal parts, what are the coordinates of the points of division?

Given the endpoints A = (3, −2, 5) and B = (3, 1, 7), find the coordinates of the midpoint of the line segment that they determine.

The coordinates of consecutive vertices of a parallelogram are A = (1, 0, 0) and B = (0, 1, 0). If the center coordinates of M are (0, 0, 1), find the coordinates for the vertices C and D.