# Midpoint (3 dimension) Calculator

Calculate the midpoint between two Entered coordinates (x

_{1}, y

_{1}, z

_{1}) and (x

_{2}, y

_{2}, z

_{2}) in three dimensional Cartesian coordinate system by averaging the XYZ coordinates.

_{1}, y

_{1}, z

_{1}) and (x

_{2}, y

_{2}, z

_{2}) points measure a linear midpoint between two locations.

### Midpoint Formula:

M = ((x_{1}+ x

_{2})/2 , (y

_{1}+ y

_{2})/2 , (z

_{1}+ z

_{2})/2)

**Therefore we can define the Midpoint with three dimention as follows:**

The line segment on the 3D coordinate plane **AB** is a part of the line that is bound by two distinct points **A _{(x1,y1,z1)}** and

**B**which are called the endpoints of the line segment

_{(x2,y2,z2)}**AB**. The point

**M**is the midpoint of the line segment

**AB**if it is an element of the segment and divides it into two congruent segments,

**AM and MB**. Each segment between the midpoint M and an endpoint have the equal length. The midpoint is the center, or middle, of a line segment. Any line segment has a unique midpoint. So, we can find the midpoint of any segment on the coordinate plane by using the mipoint formula.

$$ M(x_M,y_M,z_M)\equiv M(\frac{x_A + x_B }{2}, \frac{y_A + y_B}{2}, \frac{z_A + z_B }{2})$$ $$ or\equiv (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2})$$