## Theory. Midpoint between two points

In geometry and physics can often be faced with problems of calculation of the coordinates of midpoint, given by coordinates of endpoints, for example the problems of finding the median, the middle line, etc.

In geometry, the midpoint is the middle point of a line segment. A midpoint divides a line segment into two equal parts.

Each coordinate of the midpoint is equal to a half-sum of corresponding coordinates of endpoints A and B.

The formula for determining the midpoint of a segment in the plane, with endpoints A(x_{a}, y_{a}) and B(x_{b}, y_{b}) in Cartesian coordinates, is:

x_{c} = |
x_{a} + x_{b} |
; |
y_{c} = |
y_{a} + y_{b} |

2 | 2 |

The formula for determining the midpoint of a segment in the space, with endpoints A(x_{a}, y_{a}, z_{a}) and B(x_{b}, y_{b}, z_{b}) in Cartesian coordinates, is:

x_{c} = |
x_{a} + x_{b} |
; |
y_{c} = |
y_{a} + y_{b} |

2 | 2 |