Point

The point is a primitive concept of geometry. Intuitively equivalent to a dimensionless spatial entity, for which it may be considered simply as a position, that is, as a coordinate. In topology and calculus, any element of a topological space and, in particular, a functional space is often called a point.

A point in Euclidean geometry has no quantities of any kind (volume, area, length), and no characteristics in general except its position. Euclid’s postulates assert in some cases the existence of points; an example: if two lines in a plane are not parallel, there is exactly one point that belongs to both.

Three or more points in space are said to be aligned if they are contained in a straight line. Four or more points in space are said to be coplanar if they are contained in a plane.

Midpoint

The midpoint of a segment \(\overline{AB}\) is defined as the point \(M\) belonging to the segment itself and which measures the same distance from its ends \(A\) and \(B\). In general, in the plane, given two points \(A(x_A,y_A)\) and \(B(x_B,y_B)\), the midpoint between them is calculated with the following formulas, which provide the respective coordinates of point \(M(x_M,y_M)\):

\[x_M=\dfrac{x_A+x_B}{2}\]

\[y_M=\dfrac{y_A+y_B}{2}\]

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